Delilah S.

asked • 09/09/20# Possible Combinations

Hi! I have to figure out how many possible combinations there are with 3 objects (square, circle, triangle), 3 per row. Also, 4 objects, 3 per row. Can you help me understand how you find the answer as well without having to write out all the possible combinations? Thanks so much!

## 1 Expert Answer

THere are 3 choices for the first object, 2 choices for the 2nd, and that leaves only 1 left...

3! = 3*2*1 = 6

Now choosing 3 out of 4 , you need the formula:

n! / [(k! (n-k)!]

4!/ (3!)(1!)

= 4*3!/3! = 4

{a,b,c,d} is the set

abc, abd, acd, bcd

Delilah S.

My teacher said that for the first one it's 27 because the objects can repeat and can be in many orders. Ex. circle, circle circle; circle, circle, square; circle, square, circle; circle, square, square; circle, circle, triangle; circle, triangle, circle; circle, triangle, triangle etc. I'm not sure what that calculation would be considered as though. (It's 3x3x3 he said for 27 but I don't know why it is that. Hopefully this helps you come up with the calculations.) Also, for the second problem it's choosing 4 out of 3. Meaning, aaaa, aaab, etc.09/10/20

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Delilah S.

*3 objects, 4 per row. I apologize09/10/20