Question

The number of 5 digit numbers in which no two consecutive digits are identical is

Answer 1

We can choose the first digit any of 9 ways, 1,2,3,4,5,6,7,8 or 9 We can then choose the 2nd digit any of 9 ways, 0 or any of 8 ways not chosen for the 1st digit We can then choose the 3rd digit any of the 9 ways we didn't choose for 2nd digit. We can then choose the 4th digit any of the 9 ways we didn't choose for the 3rd digit. We can then choose the 5th digit any of the 9 ways we didn't choose for the 4th digit. That's 9·9·9·9·9 = 9⁵ = 59049