How many 8- digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 270 and no digit appears more than once?

Answer

2520

Explanation

The remaining digits to be used are 1, 2, 3, 4, 5, 6, 8, 9.
And, we have to select 5 digits out of these eight.
First digit can be anyone of these 7 digits.
So, there are 7 ways of choosing the 1st digit.
Similarly, we may choose 2nd digit in 6 ways, 3rd digit in 5 ways, 4th digit in 4 ways and 5th digit in 3 ways.
By the fundmental principle of multiplication, the required number of ways
`=(7xx6xx5xx4xx3)=2520.`