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16 May 2019, 01:10
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
80% (02:33) correct
20%
(02:31)
wrong
based on 158
sessions
History
Date
Time
Result
Not Attempted Yet
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 of the committee must come from Country A, how many distinct committees are possible?
A. 11
B. 30
C. 174
D. 200
E. 281
A. 11
B. 30
C. 174
D. 200
E. 281
Archit3110
Major Poster
16 May 2019, 02:35
Kudos
Bookmarks
Bunuel
total cases possible
5c3*6c3+5c4*6c2+5c5*6c1
200+75+6
281
IMO E
19 May 2019, 19:38
Kudos
Bookmarks
Bunuel
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
