A 4-card hand is drawn from a standard deck of 52 playing cards. Find the probability...

Question

Question

A 4-card hand is drawn from a standard deck of 52 playing cards. Find the probability that the hand contains the given cards.

exactly 4 diamonds

Answer 1

Answer #1

There are 13 diamond cards in single standard deck.

Therefore,

Number of ways to select 4 diamond cards from 13 diamond cards = ¹³C₄

Total number of ways to select 4 cards from 52 cards = ⁵²C₄

In general ⁿC_r = n! / [ ( n-r)! * r! ]

So,

P(Exactly 4 diamonds) = ¹³C₄ / ⁵²C₄

= 715 / 270725

= 0.00264

Answer 2

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