Question

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?

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.