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6.Permutation and Combination
hard
The number of four letter words that can be formed using the letters of the word $BARRACK$ is
A$144$
B$120$
C$264$
D$270$
(JEE MAIN-2018)
Solution
In the word $BARRACK$
There are $R R, A A, B, C, K$.
Number if $4$ letter words having
(i) all $4$ district letters $R, A, B, C, K=5 p_4=120$
(ii) $2$ pairs of identified letters RRAA $=\frac{4!}{2!2!}=6$
(iii) $2$ idential $2$ different $=2 \times 4 C_2 \times \frac{4!}{2!} \quad RR \quad A , B , C , K \quad=6 \times 24=144$
Total number of $4$ letter words $=120+6+144=270$
There are $R R, A A, B, C, K$.
Number if $4$ letter words having
(i) all $4$ district letters $R, A, B, C, K=5 p_4=120$
(ii) $2$ pairs of identified letters RRAA $=\frac{4!}{2!2!}=6$
(iii) $2$ idential $2$ different $=2 \times 4 C_2 \times \frac{4!}{2!} \quad RR \quad A , B , C , K \quad=6 \times 24=144$
Total number of $4$ letter words $=120+6+144=270$
Standard 11
Mathematics
