If A = {1, 2, 3, 4, 5, 6, 7}, how many elements of P(A) do not have exactly 5 elements?
Answer and explanation
Correct answer: 107
A has 7 elements, so its power set P(A) contains 2^7 = 128 subsets in total. The number of subsets having exactly 5 elements is the binomial coefficient C(7,5) = 21, because we choose 5 elements from the 7 elements of A. The required number is the total number of subsets minus these subsets: 128 − 21 = 107. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
107
Why is this the correct answer?
A has 7 elements, so its power set P(A) contains 2^7 = 128 subsets in total. The number of subsets having exactly 5 elements is the binomial coefficient C(7,5) = 21, because we choose 5 elements from the 7 elements of A. The required number is the total number of subsets minus these subsets: 128 − 21 = 107. Therefore option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
