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  4. 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

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Q. 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

Permutations and Combinations

Solution:

$\left.\left(4^5-4\right) \times 10=10200\right]$
[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 $10\left(4^5-4\right)$