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A badminton club has 21 members. What is the ratio of number of 6-memb
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11 Dec 2023, 02:29
11 Dec 2023, 02:29
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10% (02:09) wrong based on 10 sessions
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A badminton club has 21 members. What is the ratio of number of 6-member committees that can be formed from the members of the club to the number of 5-member committees that can be formed from the members of the club?
(A) 17 to 16
(B) 15 to 1
(C) 8 to 3
(D) 17 to 6
(E) 16 to 5
(A) 17 to 16
(B) 15 to 1
(C) 8 to 3
(D) 17 to 6
(E) 16 to 5
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Re: A badminton club has 21 members. What is the ratio of number of 6-memb
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12 Dec 2023, 13:05
12 Dec 2023, 13:05
2
The answer is C.
# of 6-member committees = 21C6 = 21!/(6!*15!) = 21*20*19*18*17*16/720 = 21*19*17*8
# of 5-member committees = 21C5 = 21!/(5!*16!) = 21*20*19*18*17/120 = 21*19*3*17
--> Ratio = (21*19*17*8) : (21*19*3*17) = 8 : 3
# of 6-member committees = 21C6 = 21!/(6!*15!) = 21*20*19*18*17*16/720 = 21*19*17*8
# of 5-member committees = 21C5 = 21!/(5!*16!) = 21*20*19*18*17/120 = 21*19*3*17
--> Ratio = (21*19*17*8) : (21*19*3*17) = 8 : 3
gmatclubot
Re: A badminton club has 21 members. What is the ratio of number of 6-memb [#permalink]
12 Dec 2023, 13:05
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