Shoes in the cupboard
The cupboard contains 12 distinct pairs of shoes. 4 shoes are selected at random. The probability that there is at least one matching pair from the selected shoes can be represented as , where are coprime positive integers. Find .
The answer is 202.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
There will be total ( 24 C 4 ) case
Number of ways of selection can be found by first finding number of ways in which no pair of shoes are selected and then subtracting it from total number of cases.
Number of ways selecting no pair of shoes can be found as follows:
From 12 pairs, select any 4 pairs, There are ( 12 C 4) ways to do so.
Now from these 4 selected pairs, select 1 shoe from each pair. There are 2 ways to do so. So total number of ways of selecting no pair are shoes are (12 C 4) * 16
Probability of selecting no pair of shoes is {(12 C 4)*16/(24 C 4)}
This comes out to be 120/161.
So, the probability of selecting at least one pair of shoes will be given by (1-120/161).
Hence, Answer is 41/161