# 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 Option 1) at least 500 but less than 750 Option 2) at least 750 but less than 1000 Option 3) at least 1000 Option 4) less than 500

As we learnt in

The Number of ways of Arrangement of objects -

The number of ways of n different objects taken all at a time $=\ ^{n}p_{n}=n!$

- wherein

Where 0! = 1

6 Different novels, 3 different dictionaries.

Selections are $^{6}C_{4}$ and $^{3}C_{1}$

Arrangements are 4 !

Number of such arrangements = $=\ ^{6}C_{4}\times ^{3}C_{1}\times 4!=15\times 3\times 24=1080$

Correct option is 3.

Option 1)

at least 500 but less than 750

This is an incorrect option.

Option 2)

at least 750 but less than 1000

This is an incorrect option.

Option 3)

at least 1000

This is the correct option.

Option 4)

less than 500

This is an incorrect option.

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