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i have been thinking about this problem and cant get the answer.

Can you please help me solve it?

There are 22 people and we have to make 3 groups (Financial, advertising and legal) of 5 people each.

in how many ways is this possible?

Thank you very much

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1 Answer

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For the first group pick 5 people out the 22 available in $$\binom{22}{5}$$ possible ways. Now, of the remaining $22-5=17$, take another 5 in $$\binom{17}{5}$$ ways. And finally pick 5 more out of the remaining 12: $$\binom{12}{5}$$ Multiplying these three quantities gives the answer, which will be a very large number. My calculator says it is $$129060195264$$

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