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CaptainLevi
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Amar has nine friends. He wants to invite them to his birthday party. 25 Nov 2019, 07:02
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57% (02:45) correct 43% (02:42) wrong based on 122 sessions

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Amar has nine friends. He wants to invite them to his birthday party. In how many ways can he invite at least two of his friends for his birthday party?

a) 45
b) 502
c) 511
d) 1023
e) 1100
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B
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Amar has nine friends. He wants to invite them to his birthday party. 25 Nov 2019, 09:18
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CaptainLevi
Amar has nine friends. He wants to invite them to his birthday party. In how many ways can he invite at least two of his friends for his birthday party?

a) 45
b) 502
c) 511
d) 1023
e) 1100
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Similar question : https://gmatclub.com/forum/a-man-8-frie ... l#p1843646
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CaptainLevi
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Amar has nine friends. He wants to invite them to his birthday party. 25 Nov 2019, 09:21
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gmat1393
CaptainLevi
Amar has nine friends. He wants to invite them to his birthday party. In how many ways can he invite at least two of his friends for his birthday party?

a) 45
b) 502
c) 511
d) 1023
e) 1100

Similar question : https://gmatclub.com/forum/a-man-8-frie ... l#p1843646
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Existing question :- 8 friends with at least one friend invitation
New Question :- 9 friends with at least 2 friend invitation
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Amar has nine friends. He wants to invite them to his birthday party. 26 Nov 2019, 01:53
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can anyone plz explain me this question ?
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KarishmaB
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Amar has nine friends. He wants to invite them to his birthday party. 26 Nov 2019, 03:37
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CaptainLevi
Amar has nine friends. He wants to invite them to his birthday party. In how many ways can he invite at least two of his friends for his birthday party?

a) 45
b) 502
c) 511
d) 1023
e) 1100
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Say the 9 friends are A, B, C, D, E, F, G, H, I

There are 2 ways in which he can deal with each one of his friends - he can invite them or not invite them

So there are 2 ways to deal with A - Invite A or not invite A
There are 2 ways to deal with B - Invite B or not invite B
and so on ...

So the total ways in which he can invite/not invite all his friends is 2 * 2 * 2.... (9 times) = 2^9 = 512

This includes 1 way in which he invites no one.
This also includes 9 ways in which he invites only 1 friend (invite only A, invite only B, invite only C ... and so on)

Since he must invite at least 2 friends, the cases in which no friend or only 1 friend is invited should be removed.

Total such cases = 512 - 1 - 9 = 502

Answer (B)
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Amar has nine friends. He wants to invite them to his birthday party. 26 Nov 2019, 12:04
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CaptainLevi
Amar has nine friends. He wants to invite them to his birthday party. In how many ways can he invite at least two of his friends for his birthday party?

a) 45
b) 502
c) 511
d) 1023
e) 1100
Show more


i solved with little logic and answer choices : total ways = 512 (1 yes or 1 No ) 2 ways for each 9 friends
so eliminate D and E
now we need to find at least 2 : total - none - 1 friend only ( we can see both none and 1 friend only has to be integer so answer less than 511 )
Eliminate C

left with A and B : mark B confidently as a too small
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Amar has nine friends. He wants to invite them to his birthday party. 13 Jun 2024, 15:41
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