what is the no of ways of choosing 3 cards from a pack of 52 playing cards ? In how many of these (1) three cards are of the same suit . (2) three cards belongs to three diffrent suits. (3) are face cards. (4) cards are of the same colour ?
Answers
Given : choosing 3 cards from a pack of 52 playing cards
To Find : Number of Ways
(1) three cards are of the same suit .
(2) three cards belongs to three diffrent suits.
(3) are face cards.
(4) cards are of the same colour ?
Solution:
number of ways of choosing 3 cards from a pack of 52
= ⁵²C₃ = 22100
4 Suit
three cards are of the same suit . = ⁴C₁ x ¹³C₃ = 1144
three cards belongs to three different suits
= ⁴C₃ x ¹³C₁ x ¹³C₁ x ¹³C₁
= 8788
Total Face cards = 12
face cards. = ¹²C₃ = 220
Two Colors - Red Black
cards are of the same colour
= ²C₁ x ²⁶C₃ = 5200
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