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 = 52P5 = 52x51x50x49x48 = 31,875,200

B) Size of B ({Black Red Black Red Black}, {Red, Black, Red, Black, Red}) = 26x26x25x25x24 x 2 = 20,280,000

C) Number of face values = 13

Each face value has got 4 cards

Size of C = 52x48x44x40x36 = 158,146,560

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