Consider the set S x x N and 1 lessthanorequalto x lesstha

Consider the set S = {x | (x N) and (1 lessthanorequalto x lessthanorequalto 1000)} (i.e. S = (1, 2, 3,..., 1000}). We are interested in subsets of S each of which has 10 elements. How many such subsets have only even integers ? have at least one even integer ?

Solution

a)have only even integers

S has 500 even integers

so no. of subsets of 10 elements = 500C₁₀

b)no of subsets having only odd numbers = no of subsets having only even numbers = 500C₁₀

total no of subsets with number of elemets=10 is 1000C₁₀

no of subsets with atleast one even integer=total subsets-no of subsets having only odd numbers=1000C₁₀- 500C₁₀