Topic Details (Notes format)

How to Calculate Combinations (Unordered Selections)

Subject: Mathematics

Book: Maths Mastery

Combinations focus on ways to choose k items out of n without regard to order, calculated as C(n, k) = n! / [k!(n–k)!]. For instance, to find the number of ways to select 2 fruits from {Apple, Banana, Cherry}, you have 3 choices: AB, AC, BC, which is C(3, 2) = 3. Combinations appear in scenarios like forming committees, picking lottery numbers, or combining flavors in recipes. Understanding the difference between permutations and combinations clarifies everything from business inventory groupings to advanced probability, ensuring a robust combinatorial foundation.

Practice Questions

The sum of the squares of two consecutive integers is 145. What are the integers?

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What is the sum of the interior angles of a hexagon?

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What is the sum of all even numbers between 1 and 100?

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If a+b = 10 and ab = 21, what is the value of (a-b)^2?

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If two complementary angles differ by 30°, what are the angles?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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If x^2 - 5x + 6 = 0, what are the roots?

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What is the cube root of 729?

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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If x^2 - 6x + 9 = 0, what is the value of x?

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