Question Number 100971 by john santu last updated on 29/Jun/20

A woman sent 8 letters to her   friends. The letters are kept in the  addressed envelopes at random.   The probability that 4 friends   receive correct letters and 4 letters   go to wrong destination, is ___

Answered by 1549442205 last updated on 01/Jul/20

There  are C_8 ^4  ways to choose set of four   friends that woman send correctly.For  set of four remaining friends there are   12 ways that woman send false   (4 remaining letters didn′t go to true   addresses)while there are a total 8!   ways to put letters into 8    addressed envelopes.So,P=((12.C_8 ^4 )/(8!))=(1/(48))