A COMMITTEE IS TO HAVE FOUR MEMBERS. THERE ARE SEVEN MEN AND SIX WOMEN AVAILABLE TO SERVE ON THE COMMITTEE. HOW MANY DIFFERENT COMMITTEES CAN BE FORMED?
168, 1287, 585, or 17160
The number of ways to choose 4 members out of 13 is:
$\binom{13}{4}=\frac{13!}{4!(13-4)!}=715$
Therefore, there are 715 different committees that can be formed.
The answer is not listed in the choices given, but if we assume that a typo was made and choice 1287 should have been 715, then the answer is 715.
what is the best choice
If we assume that the typo was made and choice 1287 should have been 715, then the best choice is 715.
To find the number of different committees that can be formed, we need to use the concept of combinations.
The total number of people available, which includes both men and women, is 13 (7 men + 6 women). Since we need to select 4 members for the committee, we can find the number of different committees by determining the number of combinations of 4 members that can be selected from the total pool of 13 members.
The formula for combinations is:
C(n, r) = n! / (r!(n - r)!)
where n is the total number of elements to choose from, and r is the number of elements to choose.
In this case, we need to find C(13, 4):
C(13, 4) = 13! / (4!(13 - 4)!)
= 13! / (4! * 9!)
Now we can calculate this value:
13! = 13 * 12 * 11 * 10 * 9!
Substituting these values into the formula:
C(13, 4) = (13 * 12 * 11 * 10 * 9!) / (4! * 9!)
Simplifying:
C(13, 4) = (13 * 12 * 11 * 10) / (4 * 3 * 2 * 1)
= 71,280 / 24
= 2,970
Therefore, the number of different committees that can be formed is 2,970.
So the correct answer is not in the given options.