Question

A closet contains 5 pairs of shoes. if 4 shoes are selected at random, then the probability that no complete pair of shoes is selected, is

Answer 1

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Answer 2

The probability that no complete pair of shoes is selected from the given 5 pair of shoes when 4 shoes are taken at random is 16/21.

• The probability of some event is given by the number of occurrences of the event divided the total possible number of events.

• The number of ways of drawing 4 shoes from the closet so that no complete pair of shoes is selected is by drawing 4 shoes from different pair of shoes.

• Therefore:

$^5C_4 . (^2C_1)^5$

• Now, total number of ways to select 4 shoes from the given 5 pair of shoes is:

$^{10}C_4$

• Therefore, probability of the event is

$\frac{32.(2)^5}{210}$ = $\frac{160}{210}$ = 16/21.