Combinations

Why is 6C2 equal to (6 4) ?

answer using ideas on choosing from a group

Could someone explain what this is asking and the explanation of the answer please. Anything of help is greatly appreciated.

Reply 1

latentcorpse

it's all to do with binomial coefficients and pascal's triangle of pain!
nCr= (n r) = (n!)/(r!(n-r)!)
(n r) = (n n-r) n= top number i.e. 6 in your case

6C2 = (6 2) therefore n=6 r=2
6C2 = (6 6-2)
= (6 4)

the choice form a group well basically

(6 2) represents the number of ways 2 chocolates can be chosen from a box of six chocolates and (6 4) the number of ways 4 chocoaltes cna be chosen from a box of 6.
for (6 2) = (6 4) there must be an equal number of possible combinations in each case

please rep me i'm a bit short

Reply 2

yusufu

assuming you mean 6C4:
nCr = n!/(r!(n-r)!)

6C2 = 6!/2!4!
6C4 = 6!/4!2!

hence they are equal.

Reply 3

yusufu

latentcorpse

please rep me i'm a bit short

his rep wont be worth anything.

Reply 4

latentcorpse

have u seen my rep - quote undry1 "positive rep is appreciated" - i need all i can get - i have some issues and sometimes i can get a little..........vocal!!

Reply 5

dvs

6C2 is the same as 6C4 because the number of ways you choose to pick 2 out of 6 objects is the same as the number of ways you choose NOT to pick 4 out of 6 objects.