# How many five 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?

We have to find the possible five digit numbers that are formed by the numbers 0 to 9 which starts from 67 which means first two digits are 6 and 7, when repetition of digits is not allowed.

We will use the concept of multiplication because there are sub jobs dependent on each other and are performed one after the other.

The first position from left is occupied by 6 and second position is occupied by 7 , now we have to make choices on the third , fourth and fifth position.

The third position has eight choices because out of ten 6, and 7 numbers have been used which means we are left with eight choices, for the fourth position we have seven choices because one is used in the third position, for the fifth position we have six choices left.

The number of ways in which we can form five digit numbers when two digits are fixed, and the repetition of digits is not allowed, along with given numbers 1 × 1 × 8 × 7 × 6 = 336.

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