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How many integers between 500 and 1000 contain both the digits 3 and 4?

 Aug 29, 2020
 #1
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534  543  634  643  734  743  834  843  934  943  Total =  10 such numbers

 Aug 29, 2020
 #2
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Actually, guest, though you are right, there is a way to solve this without seperatly finding each and every one of the numbers. We can use counting ;)

 

no, counting is not the type of counting you learned in preschool, it's premutations, the kind you use for combonations. 

 

We can think of the number as giant spaces:

 

–––––     ––––––    ––––––

 

The number in those amount of spaces is the possible numbers for the input:

 

    5              2              1

–––––     ––––––    ––––––

 

Now, all we have to do is multiply them all out:

 

5 * 2 * 1 = 10 possible numbers

 

And guest, you are correct. The 10 possible numbers are:

 

534  634  734  834  934   

 

543  643  743  843  943

 

:)

 Aug 29, 2020

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