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Find the number of ways of arranging the numbers 1,2 ,3, 4, 5, 6 in a row so that the product of any two adjacent numbers is at least 5.

 Jun 5, 2024
 #1
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Here's my attempt...

1 5 x x x x  and the other numbers can  be arranged in 4!  ways

1 6 x x x x  and the other numbers can be arranged in 4! ways

x x x x 5 1  and the other numbers can be arranged in 4! ways

x x x x 6 1 and the other numbers can be arranged in 4! ways

5 1 6 x x x   ....the  5 1 6  can occupy any of 4 positions and the other numbers can be arranged in 3! ways

6 1 5  x x x  ... the  6 1 5  can occupy  any of 4 positions and the other numbers can be arranged in 3! ways

 

So 

 

4 *4!   + 2* 4*3!   =   144 ways

 

cool cool cool

 Jun 6, 2024

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