If A = {p, q, r, s, t, u}, how many subsets of A contain at least 5 elements?
Answer and explanation
Correct answer: 7
The phrase “at least 5” includes subsets having exactly 5 elements and subsets having exactly 6 elements. The number of 5-element subsets is C(6,5) = 6, while the number of 6-element subsets is C(6,6) = 1. Adding them gives 6 + 1 = 7. Hence option B is correct. The empty set and smaller subsets do not satisfy the condition.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The phrase “at least 5” includes subsets having exactly 5 elements and subsets having exactly 6 elements. The number of 5-element subsets is C(6,5) = 6, while the number of 6-element subsets is C(6,6) = 1. Adding them gives 6 + 1 = 7. Hence option B is correct. The empty set and smaller subsets do not satisfy the condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
