Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

Explanation

No. of ways of selecting 1 king out of 4 kings
`= .^(4)C_(1) = 4`
No. of ways of selecting 4 cards from the remaining 48 cards `= .^(48)C_(4)`
`= (48 xx 47 xx 46 xx 45)/(4 xx 3 xx 2 xx 1) = 194580`
So, number of total groups
`= 4 xx 194580 = 778320`.