Question

There are several sets of different numbers which can be chosen from {0,1,2,3,4,5,6,7,8,9}. c How many of these sets contain any 4 numbers?

Answer 1

Answer: The number of sets contain any 4 numbers = 210

Explanation:

Given: Universal set = {0,1,2,3,4,5,6,7,8,9}.

i.e. Total choices = Numbers in set = 10

By combinations, the number of sets contain any 4 numbers =
`^(10)C_4`

`=(10!)/(4!6!)\ \ \ \ \ [^nC_r=(n!)/(r!(n-r)!)]\\\\=(10*9*8*7*6!)/(4*3*2*1 *6!)\\\\=210`

Hence, the number of sets contain any 4 numbers = 210