Question

Answer the following:

How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?

Answer 1

Digits are 0, 1, 2, ... , 9 i.e., n = 10

The first two digits in each telephone number are 45.

∴ out of six-digit telephone numbers, only 4 digits from the remaining (10 – 2) = 8 digits are to be arranged.

Hence, the number of ways in which 6-digit telephone numbers can be formed

= ⁸P₄

= 8 × 7 × 6 × 5

= 1680