Question

There are 5 letters and five addressed envelopes. the number of ways in which all the letters can be put in wrong envelopes is

Answer 1

SO 
we can solve this problem by using method of dearrangement 

=5![1-(1/1!)+(1/2!)-(1/3!)+(1/4!)+1/5!]
=the answer is 
=44

Answer 2

Answer:

44 ways

Step-by-step explanation:

There are 5 letters and five addressed envelopes. the number of ways in which all the letters can be put in wrong envelopes is

Total Number of ways = 5! = 120

The formula for the derangement can be used directly. The number of derangements is

n! (1/2!−1/3!+1/4!+…+(−1)ⁿ/n!)

Here n = 5

5 ! ( 1/2!  -  1/3!  + 1/4!   - 1/5!)

= 120 ( 1/2 - 1/6  + 1/24 - 1/120)

= 60 - 20 + 5 - 1

= 65 - 21

= 44

44 ways in which all the letters can be put in wrong envelopes