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 ^{4}C_{1}

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 ^{48}C_{4}

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

= \( \dfrac{4\times 3!}{1!\times 3!}\times \dfrac{48\times 47\times 46\times 45\times 44!}{4!\times 44!}\)

= \( \dfrac{4}{1}\times \dfrac{4669920}{24}\)

= \( 4\times 194580\)

= 778320.

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

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