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6.Permutation and Combination
hard
$BARRACK$ શબ્દના મૂળાક્ષરોનો ઉપયોગ કરી ને ચાર મૂળાક્ષરના કેટલા શબ્દ બનાવી શકાય.
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
