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

1.	What is the number of ways of choosing 4 cards from a pack In how many of these (i) four cards are of the same suit? (ii) four card belong to four different suits?
Answer» Given 52 cards → select 4 cards. (i) 4 cards are of same smit. ∴ total number of selection = [(13C₄ + 13C₄ + 13C₄ + 13C₄)/4] = 4[13C₄] = 4\|13!/(4!x 9!)\| = (4 x 13 x 12 x 11 x 10)/(4 x 3 x 2) = 2860 (ii) 4 cards are of different suits Total number of selection = 13C₁ × 13C₁× 13C₁ × 13C₁ = (134)⁴ = (13)⁴ = 28.561

What is the number of ways of choosing 4 cards from a pack In how many of these (i) four cards are of the same suit? (ii) four card belong to four different suits?

Answer»

Given 52 cards → select 4 cards.

(i) 4 cards are of same smit. ∴ total number of selection = [(13C₄ + 13C₄ + 13C₄ + 13C₄)/4]

= 4[13C₄] = 4|13!/(4!x 9!)| = (4 x 13 x 12 x 11 x 10)/(4 x 3 x 2) = 2860

(ii) 4 cards are of different suits

Total number of selection

= 13C₁ × 13C₁× 13C₁ × 13C₁

= (134)⁴ = (13)⁴ = 28.561

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What is the number of ways of choosing 4 cards from a pack In how many of these (i) four cards are of the same suit? (ii) four card belong to four different suits?

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