Question

The number of four letter words that can be formed using the letters of the word BARRACK is :

• A. 120
• B. 144
• C. 264
• D. 270

Answer 1

Answer: (D)

Given word: $BARRACK$
$B(1),A(2),R(2),C(1),K(1)$
For four letter word:
(i) All distinct letter $={}^5{C}_4\cdot 4!=120$
(ii) Two distinct letter and two alike letter $={}^2{C}_1\cdot {}^4{C}_2\cdot \frac{4!}{2!}=144$
(iii) Two alike first type letter, two alike second type $er={}^2{C}_2\cdot \frac{4!}{2!2!}=6$
Therefore, total word $=120+144+6=270$