Permutations and Combinations - Forming Numbers (Part 4) | Don't Memorise | GMAT/CAT/Bank PO/SSC CGL | Summary and Q&A

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July 13, 2015
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Permutations and Combinations - Forming Numbers (Part 4) | Don't Memorise | GMAT/CAT/Bank PO/SSC CGL

TL;DR

Understanding how to form three-digit numbers greater than 200 using 5 digits, both with and without repetition allowed.

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Key Insights

  • 💁 The condition given in the question (greater than 200) is essential to consider in forming the three-digit numbers.
  • 👻 When repetition is not allowed, the number of ways to fill each slot depends on the available digits and the condition given.
  • 👻 When repetition is allowed, each slot can be filled with any of the available digits, resulting in a higher number of possible combinations.
  • 💁 Starting with the condition (greater than 200) is a useful strategy when forming three-digit numbers with specific requirements.

Transcript

Just like what we have seen in the previous sessions, we play with these five digits. And here's our question. Take a moment and read it well! Using these five digits, how many three-digit numbers greater than 200 can be formed? Let's read it again. Three-digit numbers greater than 200. And again we have two cases. When repetition is not allowed an... Read More

Questions & Answers

Q: How many ways can the hundreds place be filled if the three-digit number has to be greater than 200?

The hundreds place can be filled with any digit greater than two, so there are four possible options: 2, 3, 4, or 5.

Q: How many ways can the tenths place be filled after using one digit in the hundreds place?

After using one digit in the hundreds place, there are four digits remaining, so the tenths place can be filled in four ways.

Q: How many ways can the unit's digit be filled after using two digits in the hundreds and tenths place?

With two digits used, there are three digits left, so the unit's digit can be filled in three ways.

Q: Does the answer change when repetition is allowed?

When repetition is allowed, the answer changes. In this case, there are 4 ways to fill the hundreds place, 5 ways to fill the tenths place, and 5 ways to fill the unit's place, resulting in a total of 100 three-digit numbers.

Summary & Key Takeaways

  • The content discusses how to form three-digit numbers greater than 200 with 5 digits, considering both cases where repetition is allowed and not allowed.

  • For the case where repetition is not allowed, there are 48 different three-digit numbers that can be formed.

  • In the case where repetition is allowed, there can be 100 three-digit numbers formed.

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