Question

What is the value of 10C3?

@karategirl2002

Answer 1

whoever gets this right I will be their fan and I will give you a medal

Answer 2

10C3 is a way of saying, "How many ways can we choose 3 things out of 10, if we don't care about the order?"

Answer 3

hurry I need the answer but I also want to know how to work it out please hurry thank you

Answer 4

To do that, we can calculate the ways to choose the first thing: 10. Times the second thing is *9, times the third thing is *8. So we have 720 ways. But we've counted some of these more than once - the ways to choose A, B, C is the same as choosing B, A, C. So for every group of 3, there are 3*2*1 ways to rearrange them that we've counted, and we need to divide by that. So our final answer is \[\frac{10*9*8}{3*2*1}\]

Answer 5

\[\huge c_3^{10} = \frac{10!}{3! (10-3)!}\]
\[\huge c_3^{10} = \frac{10!}{3! 7!}= \frac{10\times 9 \times 8 \times 7!}{3\times 2 \times 1 \times 7!}\]
\[\huge = \frac{10\times 9 \times 8}{3\times 2 \times 1}\]
\[\huge = 10\times 3 \times 4 =120\]

Answer 6

@sarahrose55

Answer 7

so it is 120? @dpasingh

Answer 8

Yes, sure

Answer 9

thank you!

Answer 10

I will see if that is right and if it is then I will become your fan and give you the medal @dpasingh

Answer 11

@sarahrose55 OK...