# Solving Combination of Variations Worksheets

How to Solve Combination Variations - Combinations are a way to estimate the total conclusions of a happening, where order of the results doesn't matter. To calculate mixtures, we use the formula, nCr = n! / r! * (n - r)!, where 'n' signifies the total number of substances, and 'r' characterizes the number of things being chosen at one time. for example I have a few empty tin cans. How many ways can I give 3 tin cans to 8 people? We have Alice, Bob and Charlie. Alice Bob Charlie = Charlie Bob Alice. For a minute, let us just figure out ways we can rearrange 3 people. Well, we have 3 choices for the first person, 2 for the second, and only 1 for the last. So, we have 3 · 2 · 1 ways to re-arrange 3 people. If you have N people and you want to find out how many arrangements there are for all of them, it is just N factorial or N! So, let us say I have 3 tin cans to give away, there are 3! or 6 variations for every option we pick. If I want to figure out how many combinations I have, I will just create all the permutations and divide by all the dismissals. In this case, I will get 336 permutations (from above), and I will divide by the 6 redundancies for each variation and get 336/6 = 56.

• ### Basic Lesson

Guides students solving equations that involve an Solving Combination of Variations. Demonstrates answer checking. A car's stopping distance varies directly with the speed, and inversely with the friction value of the road surface. If a car takes 58 feet to stop at 32 mph, on a road whose friction value is 6, what would be the stopping distance of a car traveling at 80 mph on a road with a friction value of 4?

• ### Intermediate Lesson

Demonstrates how to solve more difficult problems. Daniel must help his father carry paper rolls to the store room and the time taken for it varies directly with the number of rolls and inversely with the number of people. There are 55 paper rolls, it takes Daniel and his father 62 minutes, but if 4 of his friends join, how long will it take all of them to carry those rolls?

• ### Independent Practice 1

A really great activity for allowing students to understand the concept of Solving Combination of Variations. Time for a typing job varies directly with the number of pages and inversely with the number of copiers. It takes an average person 40 minutes to type 10 pages on the computer. If 5 average typists work together to type up 6 pages paper, how long will it take them?

• ### Independent Practice 2

Students find the Solving Combination of Variations in assorted problems. The answers can be found below. A video store rents DVDs, and the weekly total number varies directly with the total inventory, and varies inversely with the cost of each rental tape. It rented a total of 2000 DVDs when its inventory was 700 and the cost per rental was \$3.70. If its inventory does not change, what would be the effect on the weekly total number of increasing the cost per rental to \$4?

• ### Independent Practice 3

A really great activity for allowing students to understand the concept of Solving Combination of Variations. Time for a printing job varies directly with the number of pages and inversely with the number of copiers. It takes 47 minutes for 3 copiers to finish a printing job. If 7 copiers work together to print the job, how long will it take to finish?

• ### Independent Practice 4

Students find the uses for Solving Combination of Variations in assorted problems. The answers can be found below. Time for a printing job varies directly with the number of pages and inversely with the number of copiers. It takes 16 minutes for 4 copiers to finish a printing job. If 5 copiers work together to print the job, how long will it take to finish?

• ### Homework Worksheet

Students are provided with problems to achieve the concepts of Solving Combination of Variations. Time for a printing job varies directly with the number of pages and inversely with the number of copiers. If it takes 74 minutes for 4 copiers to finish a printing job. If 9 copiers work together to print the job, how long will it take to finish?

• ### Skill Quiz

This tests the students ability to evaluate data using Solving Combination of Variations. A ball is dropped from a window of a building. The distance it falls varies directly with the square of the time it falls. If a ball can fall 5 feet in 1.2 seconds, how far will it fall if it takes 2.5 seconds for it to hit the ground?