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Determine the number of 5 cards combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

$\begin{array}{1 1}(A)\;4C_1\times 48C_4\\(B)\;5C_1\times 48C_5\\(C)\;6C_1\times 48C_5\\(D)\;5C_0\times 48C_4\end{array} $

1 Answer

  • $C(n,r)=\large\frac{n!}{r!(n-r)!}$
1 king can be selected in $4C_1$ ways
4 other cards can be selected in $48C_4$ ways
$\therefore$ No of card combination out of a 52 cards each combination having exactly one king.
$\Rightarrow 4C_1\times 48C_4$
Hence (A) is the correct answer.
answered May 14, 2014 by sreemathi.v

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