Misc 6
Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.
Let the envelope be denoted by A, B, C
and the corresponding letters are a, b, c
The letters are inserted into the envelopes at random,
& each envelope contain exactly one letter
Possible combinations can be
Aa Bb Cc
Aa Bc Cb
Ab Ba Cc
Ab Bc Ca
Ac Bb Ca
Ac Ba Cb
So, Total number of possible cases = 6
n(S) = 6
Let A be the event that at least one letter is in its proper envelope
A = {(Aa, Bb, Cc), (Aa, Bc, Cb), (Ac, Bb, Ca), (Ab, Ba, Cc)}
n(A) = 4
So,
P(A) = n(A) n(S)
= 4 6
=

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.