Question

If we permute 8 letters of the word ‘computer' in 8! ways, how many permuted words have ‘p' and ‘e' next to each other?

Answer 1

answer is 2*7!..........

Answer 2

Solution:

Number of permuted words are 7! 2! = 10080

Explanation:

We have been given the word "computer" which has 8 letters and hence can be arranged in 8! ways.

Now, we have to find the number of permuted words if 'p' and 'e' are next to each other.

The things that come together can be assumed as a single unit.

Hence, {pe} can be considered as a single unit. Thus, we have now total 7 units that are {pe} {c} {o} {m} {u} {t} {r}. These can be arranged in 7! ways.

{pe} can be arranged together in 2! ways.

Therefore, number of permuted words are 7! 2! = 10080