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11 May 2020, 06:48
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E
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Difficulty:
85%
(hard)
Question Stats:
52% (02:36) correct
48%
(02:27)
wrong
based on 151
sessions
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A "standard" deck of playing cards consists of 52 cards in each of the 4 suits of Spades, Hearts, Diamonds, and Clubs. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. In how many ways 5 cards can be selected from a "standard" deck of playing cards, without a replacement, so that all 4 suits appear?
A. 1,287
B. 4,056
C. 52,728
D. 405,646
E. 685,464
Are You Up For the Challenge: 700 Level Questions
A. 1,287
B. 4,056
C. 52,728
D. 405,646
E. 685,464
Are You Up For the Challenge: 700 Level Questions
11 May 2020, 07:31
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There gonna be 1 suit of which there will be 2 cards appear.
Number of ways to select that suit = 4C1 = 4
Number of ways 5 cards can be selected from a "standard" deck of playing cards, without a replacement, so that all 4 suits appear
= 4* 13C1*13C1*13C1*13C2 = 685464
Number of ways to select that suit = 4C1 = 4
Number of ways 5 cards can be selected from a "standard" deck of playing cards, without a replacement, so that all 4 suits appear
= 4* 13C1*13C1*13C1*13C2 = 685464
Bunuel
poojakhanduja3017
Joined: 02 Dec 2018
Last visit: 01 Dec 2021
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Location: India
Schools: Goizueta '22 Wharton '22 IIMA PGPX "21 ISB '21 INSEAD Jan '20 LBS '22 Stanford '22 NUS '22 Booth '22 Cass '21
GMAT 1: 690 Q50 V32
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Schools: Goizueta '22 Wharton '22 IIMA PGPX "21 ISB '21 INSEAD Jan '20 LBS '22 Stanford '22 NUS '22 Booth '22 Cass '21
GMAT 1: 690 Q50 V32
Posts: 123
11 May 2020, 14:00
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IMO E
Concept: The formula for selecting 1 item from n items = \(nC1\)
Step 1: There will be 1 suit out of 4 in which 2 cards will be chosen
Step 2: Number of ways to select that suit = \(4C1\) = 4
Step 3: Number of ways 5 cards can be selected from the deck of playing cards, without a replacement, so that all 4 suits appear: 4* \(13C1\)*\(13C1\)*\(13C1\)*\(13C2 \)= 685,464
Concept: The formula for selecting 1 item from n items = \(nC1\)
Step 1: There will be 1 suit out of 4 in which 2 cards will be chosen
Step 2: Number of ways to select that suit = \(4C1\) = 4
Step 3: Number of ways 5 cards can be selected from the deck of playing cards, without a replacement, so that all 4 suits appear: 4* \(13C1\)*\(13C1\)*\(13C1\)*\(13C2 \)= 685,464
