Question

a pool of possible jurors consists of 14 men and 10 women. how many different juries consisting of 5 men and 7 women are possible?
a. 2,704,156
b. 0.00033069
c. 840.000331
d. 240,240
please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Calculate number of ways to choose 5 men

We use the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 14$ (number of men) and $r=5$ (number of men to choose). So $C(14,5)=\frac{14!}{5!(14 - 5)!}=\frac{14!}{5!9!}=\frac{14\times13\times12\times11\times10}{5\times4\times3\times2\times1}=2002$.

Step2: Calculate number of ways to choose 7 women

Using the combination formula with $n = 10$ (number of women) and $r = 7$ (number of women to choose). So $C(10,7)=C(10,3)$ (since $C(n,r)=C(n,n - r)$), and $C(10,3)=\frac{10!}{3!(10 - 3)!}=\frac{10!}{3!7!}=\frac{10\times9\times8}{3\times2\times1}=120$.

Step3: Calculate total number of juries

By the multiplication - principle, the total number of different juries is the product of the number of ways to choose men and women. So the total number of juries is $C(14,5)\times C(10,7)=2002\times120 = 240240$.

Answer:

D. 240,240