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
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Country A and Country B are forming a joint committee!
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student22
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This is a tough one and combinatorics aren't my strong suit, so please let me know if I did this correctly:
Since this question says that Country A has 5 people and they have to have at least 3 members, you need to test for 3 different cases:
Case 1 (Country A has 3 members): 5C3 * 6C3 = 10 * 20 = 200
Case 2 (Country A has 4 members): 5C4 * 6C2 = 5 * 15 = 75
Case 3 (Country A has 5 members): 5C5 * 6C1 = 1 * 6 = 6
Now you add the 3 cases: 200 + 75 + 6 = 281. E.
Since this question says that Country A has 5 people and they have to have at least 3 members, you need to test for 3 different cases:
Case 1 (Country A has 3 members): 5C3 * 6C3 = 10 * 20 = 200
Case 2 (Country A has 4 members): 5C4 * 6C2 = 5 * 15 = 75
Case 3 (Country A has 5 members): 5C5 * 6C1 = 1 * 6 = 6
Now you add the 3 cases: 200 + 75 + 6 = 281. E.
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Scenario 1: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
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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