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

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

JEE MainJEE Main 2018Permutations and Combinations

Solution:

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 $=120+144+6=270$