Question

Given that B=(1,2,3,4) how many subsets have exactly two elements?

Answer 1

Given that B=(1,2,3,4) how many subsets have exactly two elements?

4C2 =
     4!                4!                      4 x 3
------------ = -------------- =    --------------- = 6
 2! (4-2)!       2!  2!                    2 x 1 

answer is 6

Answer 2

The followings are the subset of {1,2,3,4}
a) {1,2,3,4} = 4 subsets
b) {12,13,14} = 3 subsets
c) {23,24} = 2 subsets
d) {34} = 1 subsets
e) {123,124,134,234} = 4 subsets
f) {1234} = 1 subsets.
g) AND DON'T FORGET THE EMPTY ELEMENT {} or {φ) = 1

In total you have 16 subsets.
Another way to calculate it quickly:
You count the number of initial elements {1234} = 4

Then you raise 2 to the power of 4: →→ 2⁴ = 16
So if you have n elements in a set you will get 2ⁿ subelements