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