Probability, Counting Methods, Permutations, and Combinations
Name:__________________________
PROBABILITY:
A bag contains 25 marbles: 10 blue, 8 red, and 7 white marbles.
1) Find the probability of picking a blue marble.
2) Find the probability of picking a red and then a blue if the marble is returned to the bag before the next
one is picked.
3) Find the probability of picking 3 white marbles if each marble is returned to the bag before the next
marble is picked.
4) Find the probability of picking 3 red marbles if each marble is NOT returned to the bag before the next
marble is picked.
COUNTING METHODS:
5) You are making your schedule for next semester and you can choose between taking 3 math classes, 4
science classes, 2 history classes and 3 English classes. How many different ways could you take 1
class of each subject?
6) How many different student ID #’s are possible if each ID contains 5 numbers from 0-9 and the
numbers are allowed to repeat?
7) How many different students ID #’s are possible in the previous problem is the numbers can not
repeat?
8) You get to choose your locker combination, it’s a 4 digit number and each digit could be a number
from 0 – 39. How many different combinations are there?
PERMUTATIONS:
9) How many ways can 8 plants of a windowsill be arranged?
10) How many ways can 9 runners place 1st, 2nd, or 3rd in a race?
11) How many ways can 10 ice cream flavors be stacked on a 2 scoop cone?
12) How many ways can you arrange the letters in “I LOVE MATH”?
COMBINATIONS:
13) How many ways can 10 ice cream flavors be put into a 3 scoop bowl?
14) How many ways can a radio station give out 15 tickets to a concert, to the 35 people who came
to the station for tickets?
15) How many ways can I remove 3 books off a shelf of 20 books?
16) How many ways can you choose 3 Captains from 11 different players on a team?