# How many words can be formed out of the letters of the word GRANDMOTHER, such that each word starts with G and ends with R?

This is a problem from a specimen question paper: "How many words can be formed out of the letters of the word GRANDMOTHER, such that each word starts with G and ends with R?"

My problem is that the question does not make it clear whether the letters can be repeated or not, and therefore, I assumed that repetition of letters is NOT allowed and this is my working:

Vowels : {A, O, E} Consonants: {G, R, N, D, M, T, H, R}

For first and last letter, we have only two choices: G and R For remaining 9 letters in between, we have 9P9 choices. Therefore, total possible words= 9P9= 362880

I would like to know if my approach and answer are correct. Also, what should I assume in regard to repetition of letters, incase questions are ambiguous as the above one?

Thanks!

• If repetition of letters were allowed, the number of possible words would be infinite. – TonyK Feb 4 '20 at 10:20

As you say, the problem is not particularly clear. What you have is correct if you are supposed to use all the letters: once you fix the G and R at the start and end, all the $$9$$ internal letters are different, so it is just the number of ways to permute them.