Question

Combinations: HELP! TELL ME WHAT IM DOING WRONG:(
A schools academic team consists of 7 students, but only two can participate in this years Knowledge slame. How many different 2- person teams can be formed from 7 students?

7!
--
(7-2)!2!

next step

7!
--
(5)!2!

so 7 x 6 x 5 x 4 x 3 x 2
-----------------
5 x 4 x 3 x 2 x 2
???
I don't know where to go from here, my answer is always wrong no matter what I do from here. I followed the combinations formal but I don't know! Help :(

Answer 1

Never mind, I just got the answer! :) 21!!

Answer 2

\[\frac{ 7! }{ 5!2! }\]
\[\frac{ 7*6*5*4*3*2*1 }{ 2*1*5*4*3*2*1 }\]
\[\frac{ 7*6 }{ 2*1 }\]
\[\frac{ 42 }{ 2 }\]

Answer 3

\[21\]

Answer 4

\[nCr=\frac{nPr}{r!}\]that tends to help me simplify those things in my own mind