Class 11 Mathematics — Chapter 6: PERMUTATIONS AND COMBINATIONS

What you'll learn

• ▸Fundamental Principle of Counting (Multiplication Principle)
• ▸Solving Counting Problems without Repetition
• ▸Solving Counting Problems with Repetition
• ▸Solving Counting Problems with Constraints
• ▸Addition Principle for Counting
• ▸Introduction to Permutations

Chapter Summary

--- PAGE 1 --- Chapter 6 PERMUTATIONS AND COMBINATIONS *Every body of discovery is mathematical in form because there is no other guidance we can have – DARWIN* 6.1 Introduction Suppose you have a suitcase with a number lock. The number lock has 4 wheels each labelled with 10 digits from 0 to 9. The lock can be opened if 4 specific digits are arranged in a particular sequence with no repetition. Some how, you have forgotten this specific sequence of digits. You remember only the first digit which is 7. In order to open the lock, how many sequences of 3-digits you may have to check with? To answer this question, you may, immediately, start listing all possible arrangements of 9 remaining digits taken 3 at a time. But, this method will be tedious, because the number of possible sequences may be large. Here, in this Chapter, we shall learn some basic counting techniques which will enable us to answer this question without actually listing 3-digit arrangements. In fact, these techniques…

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

1. Explain counting principle simply. Get Solution →
2. Give real-world permutation examples. Get Solution →
3. Find all arrangements of letters. Get Solution →
4. What is the fundamental principle of counting also known as? Get Solution →
5. According to Definition 1, what is a permutation? Get Solution →
6. What is the defined value of 0! (zero factorial)? Get Solution →
7. In the example problem from the text, how many pants and shirts does Mohan have? Get Solution →
8. What does the notation n! represent? Get Solution →

Did you know?

• 💡 There are more ways to shuffle a deck of cards than atoms on Earth.
• 💡 Lock 'combinations' are actually permutations because order matters for opening.
• 💡 A standard Rubik's Cube has over 43 quintillion possible arrangements.
• 💡 License plates use number and letter arrangements to create unique identifiers.
• 💡 There are nearly 7 quintillion unique ways to solve a Sudoku puzzle.

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