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Question
Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?
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Solution
There are 4 kings in the deck of cards.
So, we are left with 48 cards out of 52.
∴ Required combination =\[{}^{48} C_1 \times^4 C_4 + {}^{48} C_2 \times^4 C_3 + {}^{48} C_3 \times^4 C_2 + {}^{48} C_4 \times^4 C_1 \]
\[= 48 + 4512 + 103776 + 778320\]
\[ = 886656\]
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