A straight is a five card hand containing consecutive values. If m is equal to the number of ways in which all the five cards, in a straight, are not from the same suit, then the value of m 1500 is equal to (Consider the value of J as 11 , Q as 12 , K as 13 and Ace as 14 )

Step-by-step solution

Five consecutive cards can be chosen out of 13 cards in 9 ways. 2,3 , 4,5 , 6 , 3,4 , 5,6 , 7 , . . . . . . 10 , J , Q , K , A . The first card can be chosen in 4 ways (spades, hearts, diamonds and clubs). The second and the subsequent cards, too, can be chosen in 4 ways. Thus, there are 4 5 ways to choose the five cards. The number of ways in which all the five cards are not from the same suit is 4 5 - 4 = 1020 . So, the number of straights in this case is m = 9 × 1020 ⇒ m 1500 = 9 × 102 0 150 0 = 6.12