(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How many numbers betweeen 0 and 9999 have 2,5 and 8 as digitis?

3. The attempt at a solution

I have two attempts, each witha different result

The first one:

We need to arrange 4 numbers in a row such that three of the numbers are 2, 5 and 8. There are 10 options for selecting the last number and 4!=24 different arangements for a total of 10*24 = 240.

The seconed one:

In each block of 1000 numbers there are 6 combiantions. x258, x285...

We can take the seven blocks that don't start with 2 5 or 8, for 42 numbers.

Next we look at one block x--- where x is 2 5 or 8. for our purposes the blocks are symetrical so we don't need to look at them individualy.

Lets say we take the block that starts with 2

then the block 258x gives us 10

then the block 285x gives us 10

then the block 2x58 gives us 9

then the block 2x85 gives us 9

then the block 25x8 gives us 8

then the block 28x5 gives us 8

for a total of 2*(10+9+8)=52

We have three such blocks for a total of 2*52=156.

And adding the other 42 we get 198

Whats wrong here?

Thanks

Tal

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# Homework Help: How many numbers betweeen 0 and 9999 have 2,5 and 8 as digitis?

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