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Two cards are randomly selected from a pack of 52 cards. In how many ways can 2 cards be selected such that,

(1) both are of heart?

(2)one Is a king and the other is a queen?

1 Answer

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Best answer

(1) In a pack of 52 cards, there are 13 cards of heart. 2 cards of heart out of 13 cards of heart can be selected in ways.

∴ Total combinations = 13C2 × 6C3

\(\frac{13×12}{2}\)

= 20

(2) In a pack of 52 cards, there are 4 cards of king and 4 cards of queen one card of king out of 4 cards of king can be selected in 4C1 ways and one card of queen out of 4 cards of queen can be selected In 4C1 ways.

∴ Total combinations = 4C1 × 4C1

= 4 × 4

= 16

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