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6.Permutation and Combination
medium
Determine the number of $5 -$ card combinations out of a deck of $52$ cards if each selection of $5$ cards has exactly one king.
A
$^{4} C_{1} \times^{48} C_{4}$
B
$^{4} C_{1} \times^{48} C_{4}$
C
$^{4} C_{1} \times^{48} C_{4}$
D
$^{4} C_{1} \times^{48} C_{4}$
Solution
From a deck of $52$ cards, $5 -$ card combinations have to be made in such a way that in each selection of $5$ cards, there is exactly one king.
In a deck of $52$ cards, there are $4$ kings.
$1$ king can be selected out of $4$ kings in $^{4} C _{1}$ ways.
$4$ cards out of the remaining $48$ cards can be selected in $^{48} C_{4}$ ways. Thus, the
required number of $5 -$ card combinations is $^{4} C_{1} \times^{48} C_{4}$.
Standard 11
Mathematics
