Question

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.

Options

• `1/2(6!)`

• 6!

• 5⁶

• `5/2(6!)`

Answer 1

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is `underlinebb(5/2(6!))`.

Explanation:

Five digits numbers be 1, 3, 5, 7, 9

For selection of one digit, we have ⁵C₁ = 5 choice.

And six digits can be arrange in `(6!)/(2!)` ways.

Hence, total such numbers = `(5.6!)/(2!) = 5/2. 6!`