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 Question from Sean, a parent: Hi I was wondering how you would calculate how may 7 digit phone numbers there are with only odd digits?

Hi Sean,

There are 5 odd digits, 1, 3, 5, 7 and 9.

Suppose you are going to construct such a phone number starting from left to right. You have 5 choices for the first digit.

1
2
3
4
5

Regardless of which digit you chose for the first digit you have 5 choices for the second digit so the list of possible phone numbers is

11
12
13
14
15
21
22
.
.
.
55

So there are $5 \times 5$ possible 2 digit phone numbers.

Regardless of which 2 digit phone number you have you have 5 choices for the third number. How many possible 3 digit phone numbers are there?

Penny

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