Question

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How many permutations of a 7-digit phone number exist if any number 0-9 may be used but repetition is not allowed?

Answer 1

There are 604,800 possible permutations.

Explanation:

The order in which the digits are chosen is important, which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

In this question:

7 digits from a set of 10(10 digits to 0-9). So

`P_((10,7)) = (10!)/((10-7)!) = 604800`

There are 604,800 possible permutations.

Answer 2

10!/3!

Explanation:

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Because repetition is not allowed, and there are 10 initial options for the 7 decisions that need to be made, we use the formula

n!/(n-r)! = 10!/(10-7)! = 10!/3!