# Q.6.     Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

S seema garhwal

In a deck, there is 4 ace out of 52 cards.

A combination of 5 cards is to be selected containing exactly one ace.

Then, one ace can be selected in $^4C_1$ ways and other 4 cards can be selected in $^4^8C_4$ ways.

Hence, using the multiplication principle, required the number of 5 card combination $=^4C_1\times ^4^8C_4$

$=\frac{4!}{1!3!}\times \frac{48!}{44!4!}$

$=4\times \frac{48\times 47\times 46\times 45}{4\times 3\times 2}=778320$

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