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From a class of 10 students, 5 are to be chosen for a field trip. Ther

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Bunuel
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From a class of 10 students, 5 are to be chosen for a field trip. Ther [#permalink] New post   09 Feb 2021, 06:45
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From a class of 10 students, 5 are to be chosen for a field trip. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the field trip members be chosen?

A. 21
B. 28
C. 35
D. 42
E. 62
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D
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From a class of 10 students, 5 are to be chosen for a field trip. Ther [#permalink] New post   13 Feb 2021, 21:06
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Supposing all 3 will join. Then we have to choose 2 more students from the remaining 7 in 7C2 ways = 7 * 6 / 2 = 21

Supposing all 3 don't joint, then we have to choose 5 from the remaining 7 students in 7C5 = 7C2 = 21

Total number of ways = 21 + 21 = 42


Option D

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Re: From a class of 10 students, 5 are to be chosen for a field trip. Ther [#permalink] New post   15 Feb 2021, 12:35
Here is my solution for this:

Total # of ways of choosing field trip members = # of ways when all three join + # of ways when all three don't join

# of ways when all three join = There is only one way of selecting all three. The remaining 2 can be picked in 7C2 ways.
# of ways when all three don't join = There is only one way of not selecting all three. The remaining 5 can be picked in 7C5 ways.

Hence Total = (7C2*1)+(7C3*1) = 42 (D)
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From a class of 10 students, 5 are to be chosen for a field trip. Ther [#permalink] New post   01 Aug 2021, 18:23
Very confusing question. "There are 3 students who decide that either all of them will join or none of them will join" does this mean whether all the 3 won't join or these 3 students decide that none of the students join?

In that case, if they are not selected they won't allow the trip to happen.
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Re: From a class of 10 students, 5 are to be chosen for a field trip. Ther [#permalink] New post   23 May 2023, 10:27
Hello from the GMAT Club BumpBot!

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Re: From a class of 10 students, 5 are to be chosen for a field trip. Ther [#permalink]
23 May 2023, 10:27
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