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Question

The number of ways in which 52 cards can be divided into 4 sets, three of them having 17 cards each and the fourth one having just one card

A
52!(17!)3
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B
52!(17!)33!
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C
51!(17!)3
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D
51!(17!)33!
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Solution

The correct option is D 52!(17!)33!
The number of ways in which $52$52 cards can be divided into 44 sets, three of them having $17$17 cards each and the fourth one having just one card If 4n different things are to be equally distributed amongst 4 persons the numbers of ways are $4n! /(n!)4$but if 4n things are to form 4 equal groups then the
numbers of ways are.
P(E)=4n!n!44!

therefore,
Number of ways to form 4 sets, three of them having 17
Cards each and fourth just 1 card.
P(E)=52!17!33!

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