# Phone numbers

How many 7-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?

Correct result:

n =  544320

#### Solution:

$n = 9\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4 = 544320$

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Showing 1 comment:
Mathyu
Solution is not correct. 0-9 is 10 digits, so n = 10 * 9 * 8 * 7 * 6 * 5 * 4 = 604800. Or, 10!/3! = 604800. If there was a restriction on the first digit, such that the first digit could not be 0 or 1, or any other number, then it would be 9. However, there is no restriction (that is given) to make this valid, so for the first digit, there are initially 10 digits to choose from. After one is taken, then it goes to 9 and etc.

2 years ago  1 Like

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