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There are 10 pairs of shoes in a cupboard, from which 4 shoes are picked at random, then find the probability of at least one pair.
in Probability by (5 points) | 40 views

2 Answers

+2 votes
1-P(no pair)

$1-\frac{^{10}C_4\times 2^4}{^{20}C_4}$

(2^4 because you either choose left or right shoe)
by (697 points)
Hi, If I want to solve this question by first including cases of 1 pair and cases of both pair.
How will I do this?
I am not able to derive solution that way.

We can also do that way-

0 votes
you can also do it as:-

P(no pair)=$\frac{20*18*16*14}{20*19*18*17}$

because for first shoe you have 20 choices,for second shoe 18 choices,for third shoe 16 choices and for fourth shoe 14 choices.

Now, P(atleast one pair)=1-P(no pair)
by (97 points)
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