A committee is to consist of 2 members. If there are 12 men and 6 women available to serve on the committee, how many different committees can be formed?
a. 153
b. 816
c. 72
d. 136 ***
18C2 = 18*17/2 = 153
So, there must be some other conditions, if you got 136.
Too bad you didn't show your work ...
thanks bro
To find the number of different committees that can be formed, we need to use the combination formula.
The combination formula is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of objects to choose from, r is the number of objects to be chosen, and ! denotes factorial.
In this case, we have 12 men and 6 women to choose from, and we need to form a committee of 2 members.
So, using the combination formula, we have:
C(12 + 6, 2) = (12 + 6)! / (2! * (12 + 6 - 2)!)
C(18, 2) = 18! / (2! * 16!)
= (18 * 17 * 16!) / (2 * 1 * 16!)
= (18 * 17) / (2 * 1)
= 306 / 2
= 153
Therefore, the correct answer is a. 153.
To find the number of different committees that can be formed, we need to use the concept of combinations.
In this case, we have 12 men and 6 women available, and we need to choose 2 members. The number of ways to choose 2 members from a group of 12 men is given by the combination formula:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of available members, and r is the number of members to be chosen.
So, in this case, we can calculate the number of ways to choose 2 members from the group of 12 men as:
C(12, 2) = 12! / (2! * (12 - 2)!)
= 12! / (2! * 10!)
Simplifying further:
C(12, 2) = (12 * 11 * 10!) / (2! * 10!)
= (12 * 11) / (2 * 1)
= 132 / 2
= 66
Now, we need to consider the 6 women available. The number of ways to choose 2 members from this group is:
C(6, 2) = 6! / (2! * (6 - 2)!)
= 6! / (2! * 4!)
Simplifying further:
C(6, 2) = (6 * 5 * 4!) / (2 * 4!)
= (6 * 5) / (2 * 1)
= 30 / 2
= 15
Finally, to find the total number of different committees that can be formed, we need to multiply the number of ways to choose 2 men and 2 women:
66 * 15 = 990
So, the correct answer is not among the given options.