Question

To how many patrons could a telephone company furnish numbers having five digits, the first digit not being zero? I know the answer is 90,000 im just wondering how to do it

Answer 1

90,000

Explanation:

Given

A Company has to provide 5-digit numbers(The first digit≠0)

This question can be solved with Permutations and Combinations

Assume there are 5 blank spaces representing any phone number

The first digit can be filled in 9 ways(excluding 0 ={1,2,3,4,5,6,7,8,9})

The second digit can be filled in 10 ways(no exemptions={0,1,2,3,4,5,6,7,8,9})

The third digit can be filled in 10 ways(no exemptions={0,1,2,3,4,5,6,7,8,9})

The fourth digit can be filled in 10 ways(no exemptions={0,1,2,3,4,5,6,7,8,9})

The fifth digit can be filled in 10 ways(no exemptions={0,1,2,3,4,5,6,7,8,9})

So total number of ways to fill the 5 blanks

`=9*10*10*10*10\\=90000`

⇒Total number of 5-digit phone numbers= 90000