<ul class="bullet-list"><li data-list-item-id="item-1782202407227-j3n63l6gx"><div class="list-item-paragraph">\( \binom{n}{r} \) also written as&nbsp;\({}^{n} \mathrm{C} _r\), represents the number of ways to choose \(r\) items from \(n\) distinct items<br></div></li><li data-list-item-id="item-1782202407670-mnlde2y1v"><div class="list-item-paragraph">The order of selection does <strong>not</strong> matter</div></li></ul>
<p style="text-align: center">\(\binom{n}{r} = \frac{n!}{r! \times (n - r)!} = \frac{ n \times (n - 1) \times (n - 2) \times \dots \times (n - r + 1)}{r!}\)</p>
<ul class="bullet-list"><li data-list-item-id="item-1782202667383-ft5qkcd0y"><div class="list-item-paragraph">Useful identities:</div><ol class="num-list"><li data-list-item-id="item-1782202680744-epik3quoh"><div class="list-item-paragraph">\( \binom{n}{0} = 1\)</div></li><li data-list-item-id="item-1782202718778-vcagno8zs"><div class="list-item-paragraph">\( \binom{n}{1} = n\)</div></li><li data-list-item-id="item-1782202720263-03u5g4sb1"><div class="list-item-paragraph">\( \binom{n}{n-1} = n\)</div></li><li data-list-item-id="item-1782202721103-7xqzwv83q"><div class="list-item-paragraph">\( \binom{n}{n} = 1\)</div></li></ol></li></ul>

\( \binom{n}{r} \) also written as \({}^{n} \mathrm{C} _r\), represents the number of ways to choose \(r\) items from \(n\) distinct items


The order of selection does **not** matter

\(\binom{n}{r} = \frac{n!}{r! \times (n - r)!} = \frac{ n \times (n - 1) \times (n - 2) \times \dots \times (n - r + 1)}{r!}\)

Combination Formula

Combination Formula