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

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.

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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

Posted by

seema garhwal

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