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210 lines
7.7 KiB
HTML
210 lines
7.7 KiB
HTML
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<header>
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<div id="hdr"></div>
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<div id="tran"></div>
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<div id="cookOK"></div>
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<h1 class="center">Combinations and Permutations Calculator</h1>
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<p class="center"><i>Find out how many different ways to choose items.</i><br>
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<i>For an in-depth explanation of the formulas please visit <a href="combinations-permutations.html">Combinations and Permutations</a>.</i></p><br>
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<div class="script" style="height: 470px;">
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images/comb-perm.js
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</div>
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<p> </p>
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<p>For an in-depth explanation please visit <a href="combinations-permutations.html">Combinations and Permutations</a>.</p>
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<h2>Power Users!</h2>
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You can now add "Rules" that will reduce the List:
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<div class="dotpoint">
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<p><b>The "has" rule</b> which says that certain items must be included (for the entry to be included).</p>
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<p>Example: <b>has 2,a,b,c</b> means that an entry <b>must</b> have at least two of the letters a, b and c.</p>
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</div>
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<div class="dotpoint">
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<p><b>The "no" rule</b> which means that some items from the list must not occur together.</p>
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<p>Example: <b>no 2,a,b,c</b> means that an entry must <b>not</b> have two or more of the letters a, b and c.</p>
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</div>
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<div class="dotpoint">
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<p><b>The "pattern" rule</b> is used to impose some kind of pattern to each entry.</p>
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<p>Example: <b>pattern c,*</b> means that the letter c must be first (anything else can follow)</p>
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</div>
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<p>Put the rule on its own line:</p>
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<div class="example">
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<h3>Example: the "has" rule</h3>
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<p><span class="mono">a,b,c,d,e,f,g<br>
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has 2,a,b </span></p>
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<p>Combinations of a,b,c,d,e,f,g that have at least 2 of a,b or c</p>
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</div>
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<h2>Rules In Detail</h2>
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<h3>The "has" Rule</h3>
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<p><i>The word "has" followed by a space and a number. Then a comma and a list of items separated by commas.</i></p>
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<p>The number says how many (minimum) from the list are needed for that result to be allowed.</p>
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<div class="example">
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<h3>Example has 1,a,b,c</h3>
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<p>Will allow if there is an <b>a</b>, or <b>b</b>, or <b>c</b>, or <b>a and b</b>, or <b>a and c</b>, or <b>b and c</b>, or all three <b>a,b and c</b>.</p>
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<p>In other words, it insists there be an a or b or c in the result.</p>
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<p>So {a,e,f} is accepted, but {d,e,f} is rejected.</p>
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</div>
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<div class="example">
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<h3>Example has 2,a,b,c</h3>
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<p>Will allow if there is an <b>a and b</b>, or <b>a and c</b>, or <b>b and c</b>, or all three <b>a,b and c</b>.</p>
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<p>In other words, it insists there be at least 2 of a or b or c in the result.</p>
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<p>So {a,b,f} is accepted, but {a,e,f} is rejected.</p>
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</div>
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<p> </p>
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<h3>The "no" Rule</h3>
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<p><i>The word "no" followed by a space and a number. Then a comma and a list of items separated by commas.</i></p>
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<p>The number says how many (minimum) from the list are needed to be a rejection.</p>
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<div class="example">
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<h3>Example: n=5, r=3, Order=no, Replace=no</h3>
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<p>Which normally produces:</p>
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<p><b>{a,b,c} {a,b,d} {a,b,e} {a,c,d} {a,c,e} {a,d,e} {b,c,d} {b,c,e} {b,d,e} {c,d,e}</b></p>
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<p>But when we add a "no" rule like this:</p>
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<p class="mono">a,b,c,d,e,f,g<br>
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no 2,a,b</p>
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<p>We get:</p>
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<p><b>{a,c,d} {a,c,e} {a,d,e} {b,c,d} {b,c,e} {b,d,e} {c,d,e}</b></p>
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<p>The entries {a,b,c}, {a,b,d} and {a,b,e} are missing because the rule says we can't have 2 from the list a,b (having an a or b is fine, but not together)</p>
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</div>
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<div class="example">
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<h3>Example: no 2,a,b,c</h3>
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<p>Allows only these:</p>
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<p><b>{a,d,e} {b,d,e} {c,d,e}</b></p>
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<p>It has rejected any with <b>a and b</b>, or <b>a and c</b>, or <b>b and c</b>, or even all three <b>a,b and c</b>.</p>
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<p>So {a,d,e) is allowed (only one out of a,b and c is in that)</p>
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<p>But {b,c,d} is rejected (it has 2 from the list a,b,c)</p>
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</div>
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<div class="example">
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<h3>Example: no 3,a,b,c</h3>
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<p>Allows all of these:</p>
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<p><b>{a,b,d} {a,b,e} {a,c,d} {a,c,e} {a,d,e} {b,c,d} {b,c,e} {b,d,e} {c,d,e}</b></p>
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<p>Only {a,b,c} is missing because that is the only one that has 3 from the list a,b,c</p>
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</div>
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<p> </p>
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<h3>The "pattern" Rule</h3>
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<p><i>The word "pattern" followed by a space and a list of items separated by commas.</i></p>
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<p>You can include these "special" items:</p>
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<ul>
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<li><b>?</b> (question mark) means any item. It is like a "wildcard".</li>
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<li><b>*</b> (an asterisk) means any number of items (0, 1, or more). Like a "super wildcard".</li>
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</ul>
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<div class="example">
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<h3>Example: pattern ?,c,*,f</h3>
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<p>Means "any item, followed by c, followed by zero or more items, then f"</p>
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<p>So {a,c,d,f} is allowed</p>
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<p>And {b,c,f,g} is also allowed (there are no items between c and f, which is OK)</p>
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<p>But {c,d,e,f} is not, because there is no item before c.</p>
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</div>
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<div class="example">
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<h3>Example: how many ways can Alex, Betty, Carol and John be lined up, with John after Alex.</h3>
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<p>Use: n=4, r=4, order=yes, replace=no.</p>
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<div class="mono">Alex, Betty, Carol, John<br>
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pattern *,Alex,*,John </div>
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<p>The result is:</p>
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<p>{Alex,Betty,Carol,John} {Alex,Betty,John,Carol} {Alex,Carol,Betty,John} {Alex,Carol,John,Betty} {Alex,John,Betty,Carol} {Alex,John,Carol,Betty} {Betty,Alex,Carol,John} {Betty,Alex,John,Carol} {Betty,Carol,Alex,John} {Carol,Alex,Betty,John} {Carol,Alex,John,Betty} {Carol,Betty,Alex,John}</p>
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</div>
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<p> </p>
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<div class="related">
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<a href="combinations-permutations.html">Combinations and Permutations</a>
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<a href="../data/lottery.html">Lotteries</a>
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</div>
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