Question

Out of seven letters, a few of them are similar and others are different. If different words are formed taking all of them together, number of words formed is $210$, then the number of similar letters is

• A. 4
• B. 5
• C. 3
• D. 6

Answer 1

The correct option is A 4

We have seven letters and let us assume we have $n$ letter that are same. So number of ways in which we can arrange them is $\frac{7!}{n!}$

The Number of ways $=210$

So, $\frac{7!}{n!}=210$

$\Rightarrow n!=\frac{5040}{210}=24$

$\Rightarrow n=4$