Question

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

A. 3
B. 5
C. 4
D. 7

Answer 1

The total number of different letters in the word is 3.

Step-by-step explanation:

To find the total number of different letters in the word, we need to first determine the number of identical letters. Let's assume that there are 'x' identical letters and 'y' distinct letters in the word. Since there are 4 identical letters, 'x' would be 4.

Now, we can calculate the total number of different letters using the formula 'x + y = total letters'. We know that the total number of letters in the word is equal to 4 identical letters + y distinct letters = 4 + y.

Given that the total number of words that can be made with the letters is 210, we can set up an equation: 4! / (4!(4+1-y)!) = 210. Solving this equation, we find y = 3, which means there are 3 distinct letters in the word.

Therefore, the total number of different letters in the word is 3.