Question

A man is dealt a poker hand (consisting of 5 cards) from an ordinary pack of 52 playing cards. The number of ways in which he can be dealt a "straight" (a straight is five consecutive values not of the same suit, eg. $\{$ Ace $,2,3,4,5\},\{2,3,4,5,6\}$ and $\{10,J,Q,K,Ace\})$ is

• A. $4^5-4$
• B. $4!.2^{10}$
• C. $10\cdot 2^{10}$
• D. 10200

Answer 1

Answer: (D)

$\left(4^5-4\right)\times 10=10200]$
[Note: an ace can be taken in 4ways ; similarly 2 can be taken in 4 ways etc. $\Rightarrow 44^5$ ways. But this includes when they striaght consists of all five cards of the same suit $\Rightarrow \left(4^5-4\right)$. But there are 10 such straights $\Rightarrow$ Total $10\left(4^5-4\right)$