Combinations and Permutations Word Problems

TL;DR

This video provides explanations and solutions to six different combinations and permutations worded questions.

Transcript

good day welcome to the techmath channel what we're going to be having a look at in this video is some combinations and permutations worded questions this is part of a series of videos where we've been having a look at combinations and permutations uh that is a number of different ways say that we could select uh number of items from a larger group... Read More

Key Insights

• 🪈 Combinations involve selection without considering order, while permutations involve order consideration.
• ✖️ The number of possibilities in a combination or permutation can be calculated by multiplying the choices for each element.
• #️⃣ Factorials are used to calculate the number of arrangements.
• #️⃣ In permutations, circular arrangements require dividing by the number of objects being arranged.

Questions & Answers

Q: How many different ways can a person choose three songs out of seven to perform?

The person can choose the first song out of seven, then the second out of six, and the third out of five, resulting in 210 different ways.

Q: In a horse race with 12 horses, how many different ways can the first, second, and third places occur?

There are 12 possibilities for the first place, 11 possibilities for the second place (after the first place is determined), and 10 possibilities for the third place. Multiplying these gives 1,320 different ways.

Q: How many different ways can five cards be dealt from a deck of 52 cards?

Since order doesn't matter in this case, it is a combinations question. There are 52 possibilities for the first card, 51 for the second, 50 for the third, 49 for the fourth, and 48 for the fifth. Dividing by the number of arrangements gives 2,598,960 different ways.

Q: How many different ways can the letters in the word "Mississippi" be arranged?

Considering the repeats, there are 11 factorial ways to arrange the letters. Dividing by 2 factorial, 4 factorial, and 4 factorial to account for the repeats gives a total of 34,650 different ways.

Q: How many ways can four fruits be selected for a salad out of six?

This is a combinations question, so there are 6 possibilities for the first fruit, 5 for the second, 4 for the third, and 3 for the fourth. Dividing by the number of arrangements gives 15 different ways.

Q: How many different ways can six people sit around a campfire?

Since it is a circular arrangement, we assume similar arrangements if everyone moves counterclockwise. Therefore, we divide the total arrangements (6!) by 6 and get 120 different ways.

Summary & Key Takeaways

• The video discusses six combinations and permutations worded questions and provides solutions for each.

• The first question involves selecting three songs out of seven to perform, resulting in 210 different ways.

• The second question focuses on the different ways three horses can finish in a horse race, resulting in 1,320 different ways.

• The third question revolves around dealing five cards from a deck of 52 cards, resulting in 2,598,960 different ways.

• The fourth question requires arranging the letters in the word "Mississippi," accounting for repeats, resulting in 34,650 different ways.

• The fifth question involves selecting four fruits for a salad out of six, resulting in 15 different ways.

• The sixth question discusses the number of different ways six people can sit around a campfire, accounting for circular arrangements, resulting in 120 different ways.