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

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