## anonymous 5 years ago what is 10C6?

1. anonymous

This generally means how many ways can you count 6 things from 10. in this case it is 210

2. anonymous

same as $\dbinom{10}{6}$

3. anonymous

sooo 10*9*8**6*5*4/6?

4. anonymous

ok yes, as long as the 6 in your denominator is really 6*5*4*3*2

5. anonymous

and the missing 7 is a typo.

6. anonymous

25200?

7. anonymous

but there is an easier way to do this. it is fairly clear that $\dbinom{10}{6}=\dbinom{10}{4}$ since picking 6 out of ten people to invite to dinner is the same as picking 4 to exclude. it is easier to think of the second.

8. anonymous

$\frac{10\times9 \times 8\times 7}{4\times 3\times 2}$

9. anonymous

2520? or 210?

10. anonymous

or $\frac{10 \times9 \times 8\times 7\times 6\times 5\times 4}{6 \times 5 \times4 \times3\times 2}$

11. anonymous

210

12. anonymous

youre right! ty

13. anonymous

wecome. general formula is $dbinom{n}{k}=\frac{n!}{k!\times (n-k)!}$ but you really don't want to compute that way. cancel first, multiply last.

14. anonymous

oops $\dbinom{n}{k}$