1.2 Permutations and Combinations Period Date, Statistikcs and Probablity Learni

Question

1.2 Permutations and Combinations Period Date, Statistikcs and Probablity Learning Target 1.2: I understand when and how to use the Fundamental Counting Principle, Combinations, or Evaluate each COMBINATION. If you used a calculator, be sure to record what you plugged into the calculator Permutations to find the number of outcomes for an event. 1. How many ways can a student select 5 questions from an exam containing nine questions? 2. How many ways can a committee of four people be selected from a group of ten people? The general manager of a fast food restaurant chain must select 6 restaurants from 11 for a promotional program. How many different ways can the selection be done 3. 4. You want to get an ice cream sundae. You want to have 2 flavors of ice cream and 3 different toppings. If there are 10 flavors of ice cream and 8 different toppings, how many ways can you make your sundae? 5. How many different ways can you select 2 meats, 1 veggie, and 1 cheese for a sandwich from a menu that offers 5 meats, 6 veggies, and 3 cheeses? 6. There are 7 women and 5 men in a department a. How many ways can a committee of 4 be selected if it must contain 2 men and 2 women? Challenge: How many ways can a committee of 4 be selected if there must be at least 2 women on the committee? b. valuate each PERMUTATION. If you use a calculator, be sure to record what you plugged into the calculator 7. How many different four-letter permutations can be formed from the letters in the word decagon? 8. An inspector must select three tests to perform seven tests. How many ways can he perform three different tests? in a certain order on a manufactured part. He has a choice of 9. How many ways can 6 people stand in line? 0. How many ways can you arrange 3 pictures on the wall if you have 7 to pick from?

Explanation / Answer

Combination formula - nCr = n! / (r! x (n-r)!)

1) Number of ways in which a student can select 5 students from 9 = 9C5

= 9!/(5!x4!)

= 126

2) Number of ways in which a committe of 4 can be selected from 10 people = 10C4

= 10! / (4! x 6!)

= 210

3) Number of ways in which 6 restaurants can be selected from 11 = 11C6

= 462

4) number of ways to make sundae = Number of ways to chose ice cream x Number of ways to chose toppings

= 10C2 x 8C3

= 45 x 56

= 2520

P.S: please post different questions separately

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