A telephone number consists of seven digits the first three

A telephone number consists of seven digits the first three representing the exchange. How many different telelphone numbers are possible within 537 exchange?

Solution

total digits are 10 ( 1 2 3 4 5 6 7 8 9 0 )

out of seven digits the first three places are fixed with the digits 537

for the remaining four places the available digits are 7 (including 0)

hence four places can be filled 7⁴ ways ( digits can be repeated)

hence the total number of different telephone numbers possible within 537 exchange is 7⁴ = 2401