Question

how many unique 10 digit numbers can be formed if the number 2 is in the first place and repetition is allowed?

Answer 1

362880 ways

Explanation:

Given

10 digits

Required

Number of 10 digits that can be formed if no repetition and 2 must always start;

Since digit 2 must always start and no repetition is allowed, then there are 9 digits left

Digit 2 can only take 1 position

9 digits can be arranged without repetition in 9! ways;

Calculating 9!

`9! = 9 * 8 *7 * 6 * 5 * 4 * 3 * 2 * 1`

`9! = 362880`

Number of arrangement = 1 * 362880

Number of arrangement = 362880 ways