[1680] How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears

For Competitive Exams

How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?

720

360

1420

1680

Explanation:

The first two places can only be filled by 3 and 5 respectively and there is only 1 way for doing this.

Given that no digit appears more than once. Hence we have 8 digits remaining (0,1,2,4,6,7,8,9)

So, the next 4 places can be filled with the remaining 8 digits in ⁸P₄ ways.

Total number of ways = ⁸P₄=8×7×6×5=1680

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