How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

Solution:

There are 10 digits from 0 to 9.
In the 5-digit telephone number, the first two digits are 6 and 7. So only the digits from 0 to 9 other than 6 and 7 are available now.
No. of ways of filling third place = 8
No. of ways of filling fourth place = 7
No. of ways of filling fifth place = 6
By fundamental counting principle,
The number of telephone numbers that can be constructed = 8×7×6 = 336

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.1 Question 4

How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

Summary:

The number of 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once is 336