There are 5 pairs of shoes in a cupboard from which 4 shoes are picked at random. The probability that there is atleast one pair is:
(a) 8/21
(b) 11/21
(c) 12/21
(d) 13/21
Please explain if you know the solution...
Thank you!
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3 Answers
4910x9x8x7 is the no of ways to select 4 shoes!
5 R n 5 L shoes!
suppose he chooses no pair!
so the frst shoe can be chosen in 10 ways.!
the next can be chosen in 8 ways leaving the one already chosen and its pair
the next can be chosen in 6 ways leaving the ones already chosen and their pairs
the next can be chosen in 4 ways leaving the ones already chosen and their pairs.!
So, probability of not choosing a pair is 10x8x6x410x9x8x7= 821
So, probability of choosing at least one pair is 1-821 = 1321
1No. of ways to select only one correct pair = (5C1)(8 x 6)
2
No. of ways to select two correct pairs = 5C2
NO. of favourable ways = 130
Total no. of ways = 10C4 = 210
therefore probability of selecting at least one correct pair = 13/21