# Find the number of sets of six objects that can be formed from eleven objects.

neela | Student

Find the number of sets of 6 objects from 11 objects.

We know that the number of different combinations of r objects from n objects is nCr = n!/{(n-r)!*r!}, where n! = n(n-1)(n-2) [i.e.  3*2*1].

So the number of different sets of 6 objects that could be formed out of 11 objects = 11C6.

11C6 = 11!/(11-6)!6!

11C6 = 11*10*9..... 6*5*4*3*2*1/(5!)(6!)

11C6 = 11*10*9*8*7/5*4*3*2*1

11C6 = 55440/120

11C6 = 462.

Therefore it is possible to chose 462 different sets of 6 objects from 11 total objects.

11C6 = 462

giorgiana1976 | Student

We'll write the formula of the combination of n items taken k at a time:

C(n,k) = n!/k!(n-k)!

To determine the number of sets of 6 that can be formed from 11 objects, we'll apply the combination formula:

C(11,6) = 11!/6!(11-6)!

C(11,6) = 11!/6!*5!

But 11! = 6!*7*8*9*10*11

5! = 1*2*3*4*5

C(11,6) = 6!*7*8*9*10*11/6!*1*2*3*4*5

We'll simplify and we'll get:

C(11,6) = 7*8*9*11/12

C(11,6) = 7*2*3*11

C(11,6) = 462 sets of 6 that can be formed from 11 objects.