Introduction to Combinations and Permutations By Hand

TL;DR

This video explains the difference between combinations and permutations and provides formulas to calculate them.

Transcript

hello everyone in this video we're going to talk about combinations and permutations and try to clarify the differences between the two so the setup for what follows is little n is going to denote the total number of objects and they do have to be distinct so total number of distinct objects that's key so we have n different things so if you have a... Read More

Key Insights

• 🪈 Combinations are selections without considering order, while permutations involve selecting items in a specific order.
• 💁 Hiring people for the same job or forming committees are examples of combinations.
• 🥇 Determining first, second, and third place in a competition is a permutation problem.
• 😀 The formula for combinations is n choose R, and for permutations, it is nPR.
• ❓ Factorials are used in the formulas to calculate combinations and permutations.
• 🦖 n choose R can be calculated using n factorial divided by (n - R) factorial multiplied by R factorial.
• 🗂️ nPR can be calculated using n factorial divided by (n - R) factorial.

Questions & Answers

Q: What is the difference between combinations and permutations?

Combinations are selections without considering order, while permutations involve selecting items in a specific order.

Q: When would I use combinations?

Combinations are used when the order of selection doesn't matter, such as hiring people for the same job or forming committees.

Q: When is it appropriate to use permutations?

Permutations are applied when the order of selection matters, like determining first, second, and third place in a competition.

Q: What is the meaning of n choose R and nPR?

"n choose R" refers to the number of combinations when selecting R items from a group of n, while nPR represents the number of permutations when selecting R items from n.

Summary & Key Takeaways

• Combinations are selections without regard to order, such as hiring people for the same job or forming committees.

• Permutations are selections with regard to order, such as determining first, second, and third place in a race.

• The formulas for combinations and permutations are provided: n choose R and nPR, respectively.