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?

Answer 1

There are 4 kings in the deck of cards.
So, we are left with 48 cards out of 52.
∴ Required combination = ${}^{48}{C}_1{\times }^4{C}_4+{}^{48}{C}_2{\times }^4{C}_3+{}^{48}{C}_3{\times }^4{C}_2+{}^{48}{C}_4{\times }^4{C}_1$
$$\begin{gathered} =48+4512+103776+778320 \\ =886656 \end{gathered}$$