Exercise 3. Six cards are dealt from a standard deck of 52, and placed in a sequ

Question

Exercise 3. Six cards are dealt from a standard deck of 52, and placed in a sequence. (Consequently, no card is repeated.) This set, and the subsets listed below, can be counted using trees. You may give your answer as a product, to indicate how you found the formula. (A) How many sequences are there? (B) How many sequences are there in which the last card is a club? (C) How many sequences are there in which exactly one card is a club? (D) How many sequences are there in which no two members have the same face value?

Explanation / Answer

a)number of sequence =N(first card 52 ; second 51 and so on ..) =52*51*50*49*48*47

b)number of sequence =N( selecting one ut of 13 club card for last club and again select in sequence)

=13*51*50*49*48*47

c)

sleecting one club card whcih can be placed in 6 places and as rest of card is nt club therefore

number of sequence =13*6*39*38*36*35*34

d)

there are 13 ways ti select suit value and 4C2 to select 2 card of same face values which can be placed in 20 ways between rest of 4 cards ; number of sequence =13*6*20*48*44*40*36

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