Question

"a standard deck of 52 cards is shuffled thoroughly, and n cards are turned up. What is the probability that a face card turns up

Answer 1

number of face cards in a deck of 52 cards = 12

total number of cards = 52

ways of choosing 'n' cards from 52 cards = ⁵²Cⁿ = 52!/(n!)(52-n)!

ways of choosing 'n' face cards = ¹²Cⁿ = 12!/(n!)(12-n)!

Probability = favorable outcomes/total outcomes

Probability of choosing n face cards = ¹²Cⁿ/⁵²Cⁿ

Probability of choosing n face cards = (12!/(n!)(12-n)!) / 52!/(n!)(52-n)!

= [ 12! * (52-n)! ]/[ (12-n)! * 52!)