Question

5 letters are to be posted in 5 post boxes, if any number of letters can be posted in all 5 post boxes, what is the probability that each box contains only one letter?

Answer 1

Answer:

24/625

Step-by-step explanation:

Hi,

Given that 5 letters are to be posted in 5 post boxes, if any

number of letters can be posted in all 5 post boxes,

First letter could be posted in any of  5 post boxes,

Second letter can be posted in any of 5 post boxes,

Similarly an of the 5 letters can be posted in any of 5 post

boxes,

Hence, total number of ways of posting would be 5*5*5*5*5 = 5⁵

= 3125.

If it is given that each box should contain only one letter,

first letter could be posted in any of 5 boxes , where as second

shouldn't be posted in the box in which first letter had been

posted so there are 4 ways of posting second later, similarly

third letter can be posted in 3 distinct ways, fourth letter in 2

distinct ways,So total number of ways in which each box

contains only one letter would be 5*4*3*2*1 = 5! = 120

Probability that each box contains only one letter

= number of favorable ways/total number of ways

= 120/3125

= 24/625

Hope, it helps !