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NCERT Class XI Mathematics - Permutations and Combinations - Solutions

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Question : 38 of 41
Marks: +1, -0
Determine the number of 5-cards combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
Solution:  
Total no. of cards = 52, No. of cards selected = 5, No. of kings = 4
No. of other cards = 48
∴ No. of ways of selecting a king out of 4 =  4C1\,{}^{4}C_{1}
No. of ways of selecting 4 other cards out of 48 cards =  48C4\,{}^{48}C_{4}
∴ Required no. of ways =  4C1× 48C4\,{}^{4}C_{1} \times \,{}^{48}C_{4}
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