Country A and Country B are forming a joint committee!

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pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

by pkw209 » Tue Apr 20, 2010 3:30 pm

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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Source: Beat The GMAT — Problem Solving | Tue Apr 20, 2010 3:30 pm

student22: Master | Next Rank: 500 Posts; Posts: 216; Joined: Mon Dec 21, 2009 10:26 am; Thanked: 16 times

by student22 » Tue Apr 20, 2010 4:08 pm

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.

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pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

by pkw209 » Tue Apr 20, 2010 4:11 pm

Thanks Student! That's the answer I got and the same approach that I used.

Just wondering if anyone out there has another method.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8201; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun May 19, 2019 6:32 pm

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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