Question

# The number of ways in which 52 playing cards can be divided into four sets, three of them having 17 cards each and fourth are having just one card is:

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 B 52!(17!)3We have to divide 52 cards into 4 sets in which the 4th set should have only one card So, we can divide 52 cards as 17 , 17 ,17, 1 (you can see it in picture )Ways to choose 1 card form 52 card = (521)Now we have 51 card, so no. of ways to choose 17 cards from 51 cards = (5117)After this, we have 34 cards and we have to choose 17 cards from 34 cards So no. of ways to choose 17 cards from 34 cards = (3417) Now we have only 17 crads so ways to choose 17 cards from 17 cards = (1717) So, total number of ways to divide 52 card into 4 sets in which 4th set should have one card=(521)×(5117)×(3417)×(1717) And it will be equal to =52!(17!)3 Hence, option A is correct.

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