2 3 4 5 6 7 8 9 }

in how many ways you can obtain 4 pairs from the following with no pair having a GCD 2

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- May 6th 2008, 02:55 AMdhruviboynumber of ways
2 3 4 5 6 7 8 9 }

in how many ways you can obtain 4 pairs from the following with no pair having a GCD 2 - May 6th 2008, 04:20 AMSoroban
Hello, dhruviboy!

Quote:

{ 2 3 4 5 6 7 8 9 }

In how many ways you can obtain 4 pairs with no pair having a GCD 2?

. . Hence, we must form pairs in which one is odd and one is even.

We have the four odd numbers: .$\displaystyle 3\;\;5\;\;7\;\;9$

In how many ways can the even numbers be assigned?

The "2" can be paired with any of the 4 odd numbers.

Then the "4" can be paired with any of the remaining 3 odd numbers.

Then the "6" can be paired with either of the remaining 2 odd numbers.

And the "8" is paired with the 1 remaining odd number.

Therefore, there are: .$\displaystyle 4! \:=\:{\color{blue}24}$ possible pairings.

- May 6th 2008, 06:52 AMdhruviboy