Q. 314.8( 5 Votes )

# What is the number of ways of choosing 4 cards from a deck of 52 cards? In how many of these,

(a) 3 are red and 1 is black.

(b) All 4 cards are from different suits.

(c) are face cards.

(d) All 4 cards are of the same suit.

Answer :

(a) 3 are red and 1 is black

Total ways = ^{26}C_{3} × ^{26}C_{1}

= 2600 × 26

= 67600 ways

(b) All 4 cards are from different suits.

Total ways = ^{13}C_{1} × ^{13}C_{1} ×^{13}C_{1} ×^{13}C_{1}

= (^{13}C_{1})^{4}

= 13^{4}

= 28561 ways

(c) are face cards.

There are 12 face cards.

So total ways = ^{12}C_{4}

= 495 ways

(d) All 4 cards are of the same suit.

As there are 4 suits.

Total ways = ^{13}C_{4} +^{13}C_{4} + ^{13}C_{4} + ^{13}C_{4}

= 4× ^{13}C_{4}

= 2860 ways

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