Question

What is the number of permutations in which five letters a1, a2, a3, a4, a5 can be arranged such that a1 does not occupy the first and a2 does not occupy the second position?

Answer 1

Answer:

Dearr(2) = 1; Dearr(3) = 2; Dearr(4) =12 – 4 + 1 = 9; Dearr(5) = 60 – 20 + 5 – 1 = 44

Eg1.1: A person has eight letters and eight addressed envelopes corresponding to those letters. In how many ways can he put the letters in the envelopes such that exactly 5 of them get delivered correctly?

Solution: At first, select the five letters that get delivered correctly. That can be done in 8C5 ways.

Now, the other three must get delivered to the wrong address. That can be done in Dearr(3) = 2 ways.

So, total ways is 2 x 8C5 = 2 x 56 = 112 ways