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

Explanation

Since, there is exactly one ace in a combination of 5 cards, so no of ways of selecting one ace `= .^(4)C_(1) = 4`
Again, no. of ways of selecting remaining 4 cards from remaining 48 cards
`= .^(48)C_(4) = (48 xx 47 xx 46 xx 45)/(4 xx 3 xx 2xx 1) = 194580`
Therefore, number of total combinations
`= 194580 xx 4 = 778320`