Question

Find the number of words that can be formed by using all the letters in the word REMAIN. If these words are written in the dictionary order, what will be the 40^th word?

Answer 1

There are 6 letters A, E, I, M, N, R
Number of words starting with A = 5!
Number of words starting with E = 5!
Number of words starting with I = 5!
Number of words starting with M = 5!
Number of words starting with N = 5!
Number of words starting with R = 5!
Total number of words = 6 × 5! = 720
Number of words starting with AE = 4! = 24
Number of words starting with AIE = 3! = 6
Number of words starting with AIM = 3! = 6
Number of words starting with AINE = 2!
Total words = 24 + 6 + 6 + 2 = 38
39^th word is AINMER
40^th word is AINMRE