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# Peter took a 52-card deck of cards and removed all small cards, all sp

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
Peter took a 52-card deck of cards and removed all small cards, all sp  [#permalink]

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16 Aug 2018, 07:36
00:00

Difficulty:

55% (hard)

Question Stats:

59% (03:27) correct 41% (03:16) wrong based on 17 sessions

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Peter took a 52-card deck of cards and removed all small cards, all spades, and all clubs. The only remaining cards were 10, Jack, Queen, King, and Ace in the suits of heart and diamond. Of these 10 cards, he deals himself 5 cards. What is the probability that Peter deals himself at least one pair of cards?

A. 7/10
B. 17/33
C. 55/63
D. 66/165
E. 18/25

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Math Expert
Joined: 02 Aug 2009
Posts: 7112
Re: Peter took a 52-card deck of cards and removed all small cards, all sp  [#permalink]

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16 Aug 2018, 08:08
Bunuel wrote:
Peter took a 52-card deck of cards and removed all small cards, all spades, and all clubs. The only remaining cards were 10, Jack, Queen, King, and Ace in the suits of heart and diamond. Of these 10 cards, he deals himself 5 cards. What is the probability that Peter deals himself at least one pair of cards?

A. 7/10
B. 17/33
C. 55/63
D. 66/165
E. 18/25

Best way is to do 1-P(all different)
Ways all are different = 10*8*6*4*2
Ways to pick 5 out of 10 = 10*9*8*7*6
P(all different) = $$\frac{10*8*6*4*2}{10*9*8*7*6}=\frac{8}{63}$$
Ans = 1-8/63=55/63

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Peter took a 52-card deck of cards and removed all small cards, all sp &nbs [#permalink] 16 Aug 2018, 08:08
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