Question

1. Suppose set S has a cardinal number of 9.

a. How many subsets can be formed from the set?

b. How many subsets containing 5 elements can be formed from the set?

Answer 1

Given that the cardinality of set S = 9

a) Number of subsets from this set = 2⁹ = 512

General result:

If n is the number of elements in the set then

No. of subsets possible for this subset is 2ⁿ

Example. {1,2} n=2

Number of subsets = 2² =4 and those subsets are ϕ, {1}, {2},{1,2}

every set is a subset of itself i.e. {1,2}

and ϕ is a subset of every set

b) Cardinality of set is 9

So, the number of subsets containing 5 elements is 9 choose 5 =  9! / ( 5! * 4!) = 126

where n choose k is given by