A word has 4 identical letters and rest all are distinct letters. If the total number of words that can be made with the letters of the word be 210, then the total number of different letters in the word is equal to

Step-by-step solution

Let the number of distinct letters other than the identical letters be n . Total letters = n + 4 Identical = 4 , Distinct = n Number of ways in which they can be arranged = n + 4 ! 4 ! ⇒ n + 4 ! 4 ! = 210 ⇒ n + 4 n + 3 n + 2 … 6.5 = 210 = 7 × 6 × 5 ⇒ n + 4 = 7 ⇒ n = 3 So, the required number of total different letters = 3 + 1 = 4