Question

In how many ways can you choose a jury of 12 members from a group of 9 men and 11 women given the following conditions:
a) The jury is comprised of 6 men and 6 women?
b) The jury is comprised of at most 4 men?
c) The jury is comprised of at least 7 women?

Answer 1

The number of ways for 6men and 6 women is; 38,808 ways.

The number of ways format least 4 men is; 25,905 ways.

The number of ways for at most 7 women is; 67,485 ways.

What is the possible number of combinations for each scenario?

The number of ways to choose the jury of 12 members from a group of 9 men and 11 women given the following conditions are evaluated as follows;

a). For 6 men and 6 women; we have

= 9C6 × 11C6 = 84 × 462 = 38,808 ways.

b). For at most 4 men; we have;

= (9C4 ×11C8) + (9C3 × 11C9) + (9C2 × 11C10) + (9C1 × 11C11) = 20,790 + 4,620 + 396 + 99 = 25,905 ways.

c). For at least 7 women; we have;

= (9C5 × 11C7) + (9C4 ×11C8) + (9C3 × 11C9) + (9C2 × 11C10) + (9C1 × 11C11) = 41,580 + 25,905 = 67,485 ways.

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