In how many ways can the letters of the word be arranged so that there are always letters between and ?
Step 1: Form the expression representing required number of ways
The given word is .
Also given that there should always be letters between and .
Since there are a total of letters in the word .
So, the number of places for each letter are .
According to the question, the possible places of and are and .
So, the number of possible ways ,
Also, the places of and can be interchanged,
So, the number of total possible ways
After fixing the places of and , the remaining places can be filled with the remaining letters. So,
The required number of ways
Step 2: Simplify the above expression
Using the rules of permutation, the above expression can be simplified as,
The required number of ways
The required number of ways
The required number of ways
The required number of ways
Hence, the letters of the word can be arranged in ways so that there are always letters between and .