# Coding help

You are setting up a program for programming codes for a universal TV remote controller. Each code will have five digits and cannot include a 0 or repeat any digits. How many codes:

a) do not contain a 7?

b) have 3 as the third digits and 5 as the fifth digit?

c) begin with an even number?

d) begin and end with an even number?

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#### Solution Preview

a)

we have 5 free places like this: _ _ _ _ _

Now we need to fill them and count them. In the first free place, we can put numbers between 1 to 9 except for 7 which makes it 8 numbers. So up to now we have this: 8 _ _ _ _

In the next house we can put numbers between 1 to 9 except for 7 and except for the number that we put in the first house so we have 7 choices here thus up to now: 8 7 _ _ _

If we continue like this we get 8 7 6 5 4 as the number of digits (or choice of digits) that can be put in 1st to last house. Now our ...

#### Solution Summary

Coding help is embedded.