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8 people are divided evenly into 2 groups, find the number of ways to divide them?

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MathFact-orials.blogspot.com

Feb 4, 2018

70

Explanation:

This is a combination question - we don't care about the order in which people are picked. The combination formula is:

$C_{n, k} = \frac{n!}{(k!) (n - k)!}$ $C_(n,k)=(n!)/((k!)(n-k)!)$ with $n = population, k = picks$ $n="population", k="picks"$

We have 8 people and are picking 4 to be in one group (which forces the other people into the other group). That's:

$C_{8, 4} = \frac{8!}{(4!) (4!)} = \frac{8 \times 7 \times 6 \times 5}{24} = 70$ $C_(8,4)=(8!)/((4!)(4!))=(8xx7xx6xx5)/24=70$

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