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 ______.

विकल्प

• at least 500 but less than 750

• at least 750 but less than 1000

• at least 1000

• less than 500

Answer 1

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 at least 1000.

Explanation:

The number of ways in which 4 novels can be selected

= ⁶C₄

= 15

The number of ways in which 1 dictionary can be selected

= ³C₁

= 3

4 novels can be arranged in 4! ways.

∴ The total number of ways = 15 × 4! × 3

= 15 × 24 × 3

= 1080