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 ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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What is the HCF of 48 and 180?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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If 8x = 512, what is the value of x?

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If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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