Question

In how many ways can the word pacers be arranged so that each word begins with p and ends with r?

Answer 1

The word pacers can be written in many ways.

There are 6 unique letters in the word pacers, p,a,c,e,r and s. there is no repeating letter, so the word ' pacers' can be written in 6! ways.

But in this problem there is a condition such that 'each word begins with p and ends with r'. So the two positions are fixed, that is first and last position. The remaining number of positions = 6 - 2 = 4positions.

Now we have 4 positions and 4 numbers.

The number of ways these 4 numbers arranged = 4! ways =24 ways

the word 'pacers' be arranged so that each word begins with p and ends with r =  24 ways

Answer 2

Given:

Word pacer

Condition:

Each word begins with p and ends with r

Solution:

The word pacers can be permuted in many ways.

By permutation,

As pacers contain 6 characters, they can be arranged in 6! ways.

But,

According to the condition,

Two characters should remain at the same place.

And so, 6 - 2 = 4

The number of ways can the word pacers be arranged so that each word begins with p and ends with r = 4!

That is,

4 * 3 * 2 * 1 = 24 ways.