Question

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$\huge{\underline{{\textcolor{red}{Q}}{\textcolor{green}{uestion}}}}$
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

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Answer 1

Answer:

we know,

in a pack of 52 cards , there are four kings . e.g one king is selecting from 4 cards and remaining 4 cards are selecting from 48 cards.

number of ways of selecting one from 4 kings = 4C1 = 4!/1!(4-1)! = 4

number of ways selecting 4 cards out of 48 cards = 48C4 = 48!/4!.44! = 48×47×46×45/24

= 2 × 47 × 46 × 45

here, 5 cards out of 52 cards with exactly one king selected in 4C1 × 48C4 ways .

= 4 × 2 × 47 × 46 × 45

= 778320 ways .

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Answer 2

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Answer is 778320

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