If A = {1, 2, 3, 4, 5, 6),
Question:

If A = {1, 2, 3, 4, 5, 6), then the number of sub sets of A containing elements 2, 3 and 5 is _______ .

Solution:

If A = {1, 2, 3, 4, 5, 6)

i.e   n(A) = 6

Then number of subsets of A containing 2, 3, 5

i. e 3 elements is ${ }^{6} \mathrm{C}_{3}=\frac{6 !}{3 ! 3 !}$

$=\frac{6 \times 5 \times 4 \times 3 !}{3 ! 3 !}$

$=\frac{6 \times 5 \times 4}{3 \times 2}$

Then number of subsets of A

Containing 3 elements = 20