Permutations and Combinations - Forming Numbers (Part 1) | Don't Memorise | GMAT/CAT/Bank PO/SSC CGL

Summary

This video tutorial covers two common types of problems in combinatorics: forming numbers from a set of digits, both with and without repetition. It walks through step-by-step methods for calculating the number of three-digit numbers that can be formed when repetition is not allowed (resulting in 60 possible numbers) and when repetition is allowed (resulting in 125 possible numbers). The video explains how to fill slots for the hundreds, tens, and units places, highlighting the key differences in approach and illustrating how repetition can greatly increase the number of possible combinations. The tutorial emphasizes the ease of solving problems with repetition allowed.

Takeaways

• 😀 Repetition is a key concept in forming numbers, and it can significantly affect the number of possible combinations.
• 😀 When repetition is not allowed, each digit used to form the number must be unique.
• 😀 The number of ways to fill each digit slot in a three-digit number decreases as digits are used (5, 4, 3).
• 😀 Without repetition, there are 60 different three-digit numbers that can be formed using five distinct digits.
• 😀 With repetition allowed, the same digit can be used in multiple slots, resulting in more possible combinations.
• 😀 When repetition is allowed, there are 125 possible three-digit numbers that can be formed with five digits.
• 😀 The process for calculating the number of ways to form numbers follows a clear multiplication rule: multiply the available options for each slot.
• 😀 Starting with the hundreds place, tens place, or units place will lead to the same result as long as the multiplication rule is followed.
• 😀 Repetition allowed problems are easier to solve since there are fewer restrictions to consider when filling the slots.
• 😀 Understanding the difference between repetition allowed and not allowed is essential for correctly solving such problems.
• 😀 The key takeaway is that when repetition is not allowed, the total number of possible outcomes is smaller, as each digit must be distinct.

Q & A

What is the main topic discussed in the video?

The video focuses on forming three-digit numbers using a given set of digits, specifically covering scenarios where repetition is either allowed or not allowed.

What does the phrase 'repetition is not allowed' mean in this context?

In this context, 'repetition is not allowed' means that each digit used in the three-digit number must be unique, so no digit can be repeated.

How many three-digit numbers can be formed when repetition is not allowed, using five digits?

When repetition is not allowed, the total number of three-digit numbers that can be formed is 60, calculated as 5 × 4 × 3.

How do you fill the first slot in the three-digit number when repetition is not allowed?

To fill the first slot (hundreds place), you have 5 choices, as any of the five digits can be used.

What happens after filling the first slot in the 'no repetition' case?

After filling the first slot, only 4 digits remain for the second slot (tens place), and after filling the second slot, only 3 digits remain for the third slot (units place).

What is the total number of three-digit numbers when repetition is allowed?

When repetition is allowed, the total number of three-digit numbers that can be formed is 125, calculated as 5 × 5 × 5.

Why does the number of possible numbers increase when repetition is allowed?

The number increases because in the repetition allowed case, you can reuse digits in multiple slots, so there are more combinations possible.

How is the second slot filled when repetition is allowed?

In the repetition allowed case, the second slot can be filled with any of the five digits, even if the same digit used in the first slot is chosen.

Which case is easier to solve: repetition allowed or not allowed?

The repetition allowed case is easier to solve because there are no restrictions on repeating digits, simplifying the calculation.

Can the slots be filled in a different order, and will the result change?

Yes, the slots can be filled in a different order, such as starting with the units place, but the result will remain the same, as the total number of combinations is unaffected by the order in which the slots are filled.