Question

There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.

Options

• ¹²C₈

• ¹²P₈

• 2 × ¹²P₈

• 2 × ¹²C₈

Answer 1

There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to `underlinebb(2 xx ""^12C_8)`.

Explanation:

Given: 12 balls numbered from 1 to 12 we have to arrange the balls in a row either they are in ascending order or descending order at eight places.

No. of ways = ¹²C₈ + ¹²C₈

= 2 × ¹²C₈