Question

A word has 4 identical letters and others different. If the total number of words that can be made with the letters of the word be 210 then the number of different letters in the word is

• A. $3$
• B. $5$
• C. $4$
• D. $7$

Answer 1

The correct option is A $3$

Let the total number of words be n
4 are identical and remaining different
Given,
$\frac{n!}{4!}=210$
$n!=210.4!=\mathrm{3.7.5.2.4.3.2.1}=5!.3.2.7=7!$
Thus, $n=7$
Therefore, number of different letters are $3$
Hence, option 'A' is correct.