<p>In how many ways can 10 people be divided into 2 groups of 7 and 3 people?</p>
<p>thanks</p>
<p>Choosing a group of three automatically defines the group of seven, so we need only calculate the ways to choose a group of three members from a set of ten members (usually identified as 10 choose 3).</p>
<p>10 choices for the first member, 9 for the second, 8 for the third yields 720 permutations (or arrangements) of three members chosen from ten. Since we don't care about the actual arrangement of the three member set, we must divide by the number of arrangements or three members, namely six.</p>
<p>So 10<em>9</em>8/(3<em>2</em>1) = 720/6 = 120. </p>
<p>If you are punching buttons on a Ti calculator, the sequence for one step calculation would be 10 nCr 3.</p>
<p>Incidently, typing "10 choose 3" into google activates googles math calculator.</p>
<p>Sadly, most of the search hits for combinations yield pages that are opaque and unintuitive. This link is not too bad: <a href="http://mathforum.org/dr.math/faq/faq.comb.perm.html%5B/url%5D">http://mathforum.org/dr.math/faq/faq.comb.perm.html</a></p>
<p>They just through in the 3 people to through you off. If there is a group of 7 people out of ten, then the remaining group is 3 people! So it's "10 choose 7" or "10 choose 3"</p>