Question

The number of distinct arrangements that can be made by using all the letters of the word ${}^{\prime }ASPIRANT{S}^{\prime }$ such that the word begins with $T$ is

• A. $10080$
• B. $10180$
• C. $11180$
• D. $12080$

Answer 1

The correct option is A $10080$

There are $9$ letters.
$A-2,I-1,N-1,P-1,R-1,T-1,S-2$
Word has to begin with $T.$
It can be done in only $1$ way.
Remaining $8$ letters can be arranged in $\frac{8!}{2!2!}$ ways.
So, total number of ways $=1\times \frac{8!}{2!2!}=10080$