How many 6-digit telephone numbers can be constructed with digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?
Given, numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9
The total number of these digits are 10
To find: 6-digit telephone numbers starting with 35 and no digit appears more than once
So, fix the position of first two digits as 3 and 5
Now, we need to fill these 4 remaining places
Remaining number of digits are 8 (0, 1, 2, 4, 6, 7, 8, 9)
Arrange these 8 numbers at 4 places.
Formula used:
Number of arrangements of n things taken r at a time = P(n, r)
∴ The total number of ways
= the number of arrangements of 8 things taken 4 at a time
= P(8, 4)
= 8 × 7 × 6 × 5
= 1680
Hence, possible number of 6-digit telephone numbers starting with 35 are 1680