Activity 12-22: Combinations Name:
An arrangement or listing in which order is not important is called a combination.
Example: Mr. Mangham is giving away 3 movie tickets. There are 7 different students with Mangham’s Most Wanted slips from which Mr. Mangham will draw. How many possible ways can Mr. Mangham pick the 3 winners for the prizes?
A quick way to find the number of combinations is to divide the number of permutations, 7 P3 , by the number of orders 3 students can be drawn, 3!.
Numberofways= 7•6•5=210=35ways 3•2•1 6
n Cr means the number of combinations of n things taken r at a time. n C r = n Pr
Find each value.
1. 4C2 4. 8C3
2. 5C3 5. 6C4
3. 6C2 6. 7C7
r!
7. 15C6
Determine whether each situation is a permutation or a combination.
10. Annie taking 2 drinking glasses from 6 on a shelf
11. Finnick placing 6 different drinking glasses on a shelf
12. President Snow taking 4 cards from a 52-card deck
13. A mutt choosing 3 numbers from 1 to 9
A mockingjay making a 3 digit number with each digit between 1 and 9 and each digit only used once
Solve.
8. 15C7
9. 15C8
14.
How many ways can you choose four toy soldiers from a collection of sixteen toy soldiers?
15.
16. How many different five-card hands are possible using a 52-card deck?
17. 18.
19. 20.
How many combinations of four textbooks can be chosen from eight textbooks in a locker?
How many different “double features” (two-film showings) can be chosen from a collection of twelve films?
How many ways can 5 children line up to get on the school bus if Jenny always gets third?
Write your own interesting word problem which can be solved by a combination.
Created by Lance Mang