Hey guys need help with this question..

Let

S = {0,1,2,....,20}

(a) How many subsets of S are there?

(b) How many subsets of S contain numbers divisible by 3?

(c) How many subsets of S contain 7, 9 and 15?

(d) How many subsets of S do not contain 7, 9 and 15?

(e) How many subsets of S contain 7, 9 and 15 but not 11 and 12?

(b) How many subsets of S contain numbers divisible by 3?

(c) How many subsets of S contain 7, 9 and 15?

(d) How many subsets of S do not contain 7, 9 and 15?

(e) How many subsets of S contain 7, 9 and 15 but not 11 and 12?

**My Solutions**

a) \(\displaystyle \sum_{i=0}^{20} = \binom{20}{i}\)

b) \(\displaystyle \sum_{i=0}^{7} = \binom{7}{i}\)

c) \(\displaystyle \sum_{i=0}^{3} = \binom{3}{i}\)

d) \(\displaystyle \sum_{i=0}^{18} = \binom{18}{i}\)

e) c) \(\displaystyle \sum_{i=0}^{3} = \binom{3}{i}\)

Are my solutions correct? thanks

Are my solutions correct? thanks