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

Solution :

The number of ways in which 4 novels can be selected = \(^6C_4\) = 15

The number of ways in which 1 dictionary can be selected = \(^3C_1\) = 3

Now, we have 5 places in which middle place is fixed.

\(\therefore\)  4 novels can be arranged in 4! ways

\(\therefore\)  total number of ways = 15 \(\times\) 4! \(\times\) 3

= 15 \(\times\) 24 \(\times\) 3

= 1080


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