Suppose that you have 20 different letters and 10 distinctly

Suppose that you have 20 different letters and 10 distinctly addressed envelopes. The 20 letters consist of lo pairs, where each pair belongs inside one of the 10 envelopes. Suppose that you place the 20 letters inside the lo envelopes, two per envelope, but at random. What is the probability that exactly 3 of the lo envelopes will contain both of the letters which they should contain?

Solution

Ans: In order to get exactly 3 out of 10 envelopes containing the correct pair of letters , we have

Number of ways in which Correct pair being chosen =
(20-2*3)! / 2^(10-3)

Total number of ways of being chosen= 20! / 2^10

Thus probability of exactly 3 out of 10 envelopes containing the correct pair of letters,

= [ (20-2*3)! / 2^(10-3) ] / [20! / 2^10]

On calculation we get probability = 2.866*10^(-7)