# Different Combinations

• May 18th 2007, 09:54 PM
Chilly_101
Different Combinations
I have a question:
You have 10 slots in which to put the numbers 1-5 and each number must be used twice but no more than twice. (ex: 5 5 4 4 3 3 2 2 1 1 ex. 5 4 5 3 2 4 1 2 1 3.) How many different combinations are there? ( I think i know the answer but i just want to double check)
• May 19th 2007, 03:44 AM
Plato
Have you tried [10!]/[2^5]?
• May 19th 2007, 05:01 AM
Chilly_101
No i didnt, is that the answer?
• May 19th 2007, 07:06 AM
Soroban
Hello, Chilly!

Plato is absolutely correct . . .

Quote:

You have 10 slots in which to put the numbers 1 to 5'
and each number must be used twice but no more than twice.
How many different permutations are there?

Suppose we had ten different numbers.
. . There would be 10! arrangements.

But since there two 1's, they can be switched without creating a new arrangement.
. . Hence, they make our answer too large by a factor of 2.

And since there two 2's, they too can be switched.
. . Hence, they make our answer too large by a factor of 2.

Similarly, two 3's, two 4's and two 5's can be switched.
. . Each makes the answer too large by a factor of 2.

Hence, our answer is too large by a factor of 2^
5.

. . - . . - . . - . . 10!