Let S be the set of sequences of five cards, in which no card is repeated. You c

Question

Let S be the set of sequences of five cards, in which no card is repeated. You can think of it as all the ways to deal five cards, where the order of the deal matters. What is the size of S? Let B be the subset of sequences in which the color of the card alternates. For example, if the first card is black, then the second is red, the third is black and so on. What is the size of B? Each card has one of thirteen 'face value'. A face value may be the number of 'pips', such as two or seven. In addtion, there are four special face values: ace, king, queen and jack. Let C be the subset of sequences in which the five cards have five different face values. What is the size of C?

Explanation / Answer

(A) size of S is nothing but the number of permutations of five numbers which is equal to 52P5

where npr = n*n-1*.... (n-r+1)

(B) It is permutating 3 black cards and red cards in 1,3,5 and 2,4 positions repsectively. =number of ways of selecting 3 black cards and permutating and number of ways of selecting 2 red cards and permutating.

Hence the size of B = 26P3 * 26P2

(C)We first chose one of four from diamonds, heart,spades and clubs and permutate the 5 cards from 13 different face values, hence the number of ways we can do it is 4*13P5

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