How many seven-digit phone numbers can be formed if the first digit cannot be 0 and repetition of digits is not permitted?

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Answer 1 · 2016-01-28T01:06:16

Take it step-by-step ...

There are 9 ways to pick the first digit [1-9]

Next, there are 9 ways to pick the second digit [0 plus the remaining 8 from the first digit]

The 3rd digit is chosen from the remaining 8 numbers.

The 4th digit is chosen from the remaining 7 numbers.

The 5th digit is chosen from the remaining 6 numbers.

The 6th digit is chosen from the remaining 5 numbers.

The 7th digit is chosen from the remaining 4 numbers.

So, in summary, there are ...

$9 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4$ $9xx9xx8xx7xx6xx5xx4$ ways $= 544320$ $=544320$ ways

hope that helped