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From 6 different novels and 3 different ...

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. Then the number of such arrangements is (1) less than 500 (2) at least 500 but less than 750 (3) at least 750 but less than 1000 (4) at least 1000

A

atleast 1000

B

less than 500

C

atleast 500 but less than 750

D

atleast 750 but less than 1000

Text Solution

Verified by Experts

The correct Answer is:
A
Given 6 different novels and 3 different dictionaries.
Number of ways of selecting 4 novels from 6 novels is
`""^(6)C_(4) = (6!)/(2!4!) = 15`
Number of ways of selecting 1 dictionary is from 3 dictionaries is `""^(3)C_(1) = (3!)/(1!2!) = 3`
`therefore` Total number of arrangement of 4 novels and 1 dictionary where dictionary is always in the middle, is
`15 xx 3 xx 4! = 45 xx 24 = 1080`
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