What makes a number binomial?: Subsets

We'll divide the number of subsets into 5 cases:

$0$ members : $\binom{4}{0} = 1$

$1$ member: $\binom{4}{1} = 4$

$2$ members: $\binom{4}{2} = 6$

$3$ members: $\binom{4}{3} = 4$

$4$ members: $\binom{4}{4} = 1$

Thus there are $1 + 4 + 6 + 4 + 1 = \boxed{16}$

It's relatively simple. A set with n elements have 2^n subsets. In this case, there are 4 elements, so 2^4=16.

Every element has got $2$ choices. Whether to be a part of subset or not .

So , by multylping we get $2.2.2.2 =2^4=16$ .