Question

If $3$ are alike and one is different

• A. $30$
• B. $28$
• C. $35$
• D. $42$

Answer 1

Answer: (B)

$28$

Out of the given letters only $1$ letter repeats thrice $\left(I\right).$ We are asked to find words containing $3$ alike letters $\xi$ one different. Since only $I$ repeats thrice $=1$ way.

$\Rightarrow$ We need to choose the other letter from remaining $7$ district letters $={}^7{C}_1=7$

$\Rightarrow$ Total $1\times 7=7$

Now, these letters can be arranged in $\frac{4!}{3!}$

$\Rightarrow$ Ways $=4$

$\therefore$ Required $=7\times 4=28.$

Hence, the answer is $28.$