What is the number of ways to choosing 4 cards from a pack of 52 cards

1.	What is the number of ways to choosing 4 cards from a pack of 52 cards ? In how many of these(1) Four cards are of same suit.(2) Four cards belong to four different suits.(3) Four face cards.(4) Two cards are red cards and two are black cards.
Answer» No of ways of choosing 4 cards = ⁵²C₄ = 270725 (1) No. of ways of choosing 4 cards of same suit = 13C₄ + 13C₄ + 13C₄ + 13C₄ = 2860 (2) No. of ways of choosing cards of different suits = 13C₁ x 13C_{1 x} 13C₁ x 13C₁ = 28561 (3) No. of ways of choosing 4 face cards = ¹²C₄ = 495 (4) No. of ways of choosing 2 red and 2 black cards = ²⁶C₂ x ²⁶C₂ = 105625

What is the number of ways to choosing 4 cards from a pack of 52 cards ? In how many of these(1) Four cards are of same suit.(2) Four cards belong to four different suits.(3) Four face cards.(4) Two cards are red cards and two are black cards.

Answer»

No of ways of choosing 4 cards = ⁵²C₄ = 270725

(1) No. of ways of choosing 4 cards of same suit

= 13C₄ + 13C₄ + 13C₄ + 13C₄ = 2860

(2) No. of ways of choosing cards of different suits

= 13C₁ x 13C_{1 x} 13C₁ x 13C₁ = 28561

(3) No. of ways of choosing 4 face cards

= ¹²C₄ = 495

(4) No. of ways of choosing 2 red and 2 black cards

= ²⁶C₂ x ²⁶C₂ = 105625

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What is the number of ways to choosing 4 cards from a pack of 52 cards ? In how many of these(1) Four cards are of same suit.(2) Four cards belong to four different suits.(3) Four face cards.(4) Two cards are red cards and two are black cards.

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