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How many seven-digit positive integers satisfy the following conditions?

The integer contains the digits 1,2,3,4,5,6  and 7 exactly once each.

The numbers 1,2 and3  appear in that order within the digits of the number. (They do not need to be consecutive digits.)

For example, two such integers are 7162534  and 1245673

 

 Aug 9, 2022
 #1
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Not great at these counting problems but here's my best attempt

 

Choose  any 3 of 7 positions for the digits 1,2,3  =  C(7,3)  = 35

 

For the other positions the other digits can be arranged in 4! =  24 ways

 

So....the total number of integers =     35 * 24  =   840

 

cool cool cool

 Aug 9, 2022

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