A business organization needs to make up a 7 member fund-raising committee. The organization has 6 accounting majors and 7 finance majors. In how many ways can the fund-raising committee be formed if at least 4 accounting majors are on the committee?

Question

Mathematics

Winter

6 April, 08:13

A business organization needs to make up a 7 member fund-raising committee. The organization has 6 accounting majors and 7 finance majors. In how many ways can the fund-raising committee be formed if at least 4 accounting majors are on the committee?

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Answers (1)

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Jaylyn Forbes · Answer 1

Answer: 658 ways.

Step-by-step explanation:

To find the number of ways the number "r" items can be chosen from the available number "n", the combination formula for selection is used. This formula is denoted as:

nCr = n! / (n-r) ! * r!

Where n! = n * (n-1) * (n-2) ... * 3*2*1.

If we have 6 accounting majors and 7 finance majors and we are to choose a 7-member committee from these with at least 4 accounting majors on the committee, then the possibilities we have include:

[4 accounting majors and 3 finance majors] Or [5 accounting majors and 2 finance majors] or [ 6 accounting majors and 1 finance major].

Mathematically, this becomes:

[6C4 * 7C3] + [6C5 * 7C2] + [6C6*7C1]

525 + 126 + 7 = 658 ways.

Note: it is 6C4 because we are choosing 4 accounting majors from possible 6. This applies to other selection possibilities.