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What is the number of ways of choosing 4 cards from a pack of

Question

What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these four cards are of the same suit.

2860

715

270275

1430

none of these

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What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these four cards are of the same suit.

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Text solutionVerified

The number of ways of choosing

4

cards from a pack of

52

playing cards

=^{52} C_{4} = \frac{52 !}{4 ! 48 !} = \frac{52 \times 51 \times 50 \times 49}{1 \times 2 \times 3 \times 4} = 270725

The number of ways of choosing

4

cards of same suit

=^{13} C_{4} = \frac{13 !}{4 ! 9 !} = \frac{13 \times 12 \times 11 \times 10}{1 \times 2 \times 3 \times 4} = 715

Since there are

4

suits, therefore, the number of ways of choosing

4

cards of one suit

= 4 \times 715 = 2860

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Question Text	What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these four cards are of the same suit.
Answer Type	Text solution:1
Upvotes	150