Permutation and CombinationEasy
Question
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is
Options
A.less than 500
B.at least 500 but less than 750
C.at least 750 but less than 1000
D.at least 1000
Solution
4 novels can be selected from 6 novels in 6C4 ways. 1 dictionary can be selected from 3 dictionaries in 3C1 ways. As the dictionary selected is fixed in the middle, the remaining 4 novels can be arranged in 4! ways.
∴ The required number of ways of arrangement = 6C4 × 3C1 × 4! = 1080
∴ The required number of ways of arrangement = 6C4 × 3C1 × 4! = 1080
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