pkw209 wrote:Country A and Country B will form a joint committee on economic policy. The committee is to have exactly 6 members. 5 candidates for the committee come from Country A and 6 from Country B. If at least 3 members o the committee must come from Country A, how many distinct committees are possible?
A) 11
B) 30
C) 174
D) 200
E) 281
Scenario 1:
3 A and 3 B
3 As can be selected in 5C3 ways:
(5 x 4 x 3)/3! = 10
3 Bs can be selected in 6C3 ways:
(6 x 5 x 4)/3! = 20
The total number of ways is 10 x 20 = 200.
Scenario 2:
4A and 2 B
4 As can be selected in 5C4 = 5 ways.
2 Bs can be selected in 6C2 ways:
(6 x 5)/2! = 15
The total number of ways is 5 x 15 = 75.
Scenario 3:
5 A and 1 B
5 As can be selected in 5C5 = 1 way.
1 B can be selected in 6C1 = 6 ways.
The total number of ways is 1 x 6 = 6.
So the total number of ways to create a committee of 6, with at least 3 members from Country A, is 200 + 75 + 6 = 281.
Answer: E
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