Permutations and Combinations 4 Question 3
3. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf, so that the dictionary is always in the middle. The number of such arrangements is
(2018 Main)
(a) atleast 1000
(b) less than 500
(c) atleast 500 but less than 750
(d) atleast 750 but less than 1000
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Answer:
Correct Answer: 3. (a)
Solution:
- Given 6 different novels and 3 different dictionaries.
Number of ways of selecting 4 novels from 6 novels is
$$ { }^{6} C _4=\frac{6 !}{2 ! 4 !}=15 $$
Number of ways of selecting 1 dictionary is from 3 dictionaries is ${ }^{3} C _1=\frac{3 !}{1 ! 2 !}=3$
$\therefore$ Total number of arrangement of 4 novels and 1 dictionary where dictionary is always in the middle, is
$$ 15 \times 3 \times 4 !=45 \times 24=1080 $$
