Jackson asked in Science & MathematicsMathematics · 2 months ago

# A 5 member committee is to be formed from 6 boys and 4 girls. If the committee must include exactly 2 girls. How many committee is forced? ?

Update:

A 5 member committee is to be formed from 6 boys and 4 girls. If the committee must include exactly 2 girls. How many committee is formed?

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• TomV
Lv 7
2 months ago

The committee will be formed from 2 girls selected from a pool of 4, C(4,2), and 3 boys selected from a pool of 6, C(6,3).

The total number of unique committees that can be formed is:

N = C(4,2)•C(6,3) = [4!/(2!)²] • [6!/(3!)²] = (3*2)•(5*4) = 6*20 = 120

Ans: 120

Ref: C(m, n) = m!/[n!(m-n)!]

• 2 months ago

If there are 2 girls, then there are 3 boys

Girl choices => 4C2 = 6

Boy choices => 6C3 = 20

Total is 6 x 20 = 120 committees

:)>

• 2 months ago

There's only one committee.

Maybe I don't understand the question.  To get a good answer, you have to ask the question here exactly as it was presented to you.