Question

The number of arrangements that can be made using all the letters of the word ${}^{\prime }QUART{Z}^{\prime }$ which begin with A but do not end with R is

• A. $36$
• B. $96$
• C. $48$
• D. $24$

Answer 1

The correct option is B $96$

Given letters are $Q,U,A,R,T,Z=6$ letters.

We need to find $6$ lettered words that start with $A$ and does not end with $R.$

The first letter is fixed $\left(A\right),$ the last letter can be any of the remaining $5$ except $R.$

So, we have $4$ choices for the last letter.

For the remaining $4$ places, the $4$ remaining letters can be used in $4!$ ways.

$\Rightarrow$ Total $=4\times 4!=96.$

Hence, the answer is $96.$