Homework SourseHow many subsets of 1 2 3 4 5 6 7 8 9 have equal numbers of
How many subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} have equal numbers of odd elements as even elements?
ex: {2,3} {2,3,4,5}
Solution
there are 5 odd and 4 even numbers.
No. of subsets containing 2 elements = 5C1 * 4C1 = 20
No. of subsets containing 4 elements = 5C2 * 4C2 = 60
No. of subsets containing 6 elements = 5C3 * 4C3 = 40
No. of subsets containing 8 elements = 5C4 * 4C4 = 5
total = 20 + 60 + 40 + 5 = 125
