Instead of one committee, we decide to form two six-person committees. Each employee can be on at most one committee. How many ways can we form these committees, if employee happiness is not taken into consideration?

Question

Mathematics

Tanner Hanson

3 February, 04:11

Instead of one committee, we decide to form two six-person committees. Each employee can be on at most one committee. How many ways can we form these committees, if employee happiness is not taken into consideration?

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Answers (1)

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Emma · Answer 1

116,396,280 ways

Step-by-step explanation:

Two six-person committees are to be formed from 20 people.

The first 6 person committee can be formed in

²⁰C₆ ways = 38760 ways.

After forming this committee, there are 14 people left.

The second 6 person committee can be formed in

¹⁴C₆ ways = 3003 ways

The two committees can be formed in

38760 * 3003 ways = 116,396,280 ways