Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

Asked by Pragya Singh | 1 year ago |  74

##### Solution :-

Given a deck of 52 cards

There are 4 Ace cards in a deck of 52 cards.

According to question, we need to select 1 Ace card out the 4 Ace cards

Number of ways to select 1 Ace from 4 Ace cards is 4C1

More 4 cards are to be selected now from 48 cards (52 cards – 4 Ace cards)

Number of ways to select 4 cards from 48 cards is 48C4

$$\dfrac{4!}{1!(4-11)!}\times \dfrac{48!}{4!(48-4)!}=\dfrac{4!}{1!\times 3!}\times \dfrac{48!}{4!\times 44!}$$

$$\dfrac{4\times 3!}{1!\times 3!}\times \dfrac{48\times 47\times 46\times 45\times 44!}{4!\times 44!}$$

$$\dfrac{4}{1}\times \dfrac{4669920}{24}$$

$$4\times 194580$$

= 778320.

Number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination 778320.

Answered by Abhisek | 1 year ago

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