Question

How many subsets of four elements each exist in a set of seven elements?

Answer 1

The answer is C7,4 = 7x6x5x4/4! = 7x5 = 35

Answer 2

C(7, 4) = 35

Explanation:

This is called combination.

The total number of elements (n) = 7

The number elements in a subset(r) = 4

The number of subsets = C(7, 4)

= 7!/4!(7 -4)!

= 7!/4!3! [7! = 5040, 4! = 24, 3! = 6]

= 5040 / (24*6)

= 5040/144

= 35 ways

Answer is C(7, 4) = 35

Hope this will helpful.

Thank you.