Download Notes #13 – The Multiplication Rule

Statistics and Probability
Multiplication Rule Notes
Name: ________________________________
Date: ________________________________
Fundamental Counting Principle:
If one event can occur “m” ways and another event can occur “n” ways, then the number of ways both can
occur is:
Example #1: In the morning, you have 4 shirts and 3 pairs of pants to choose from to make an outfit.
a) Draw a diagram that represents all possible arrangements of outfits possible.
b) What is the total number of outfits? What do you notice about the total number? Do you see a
way to do this that might be easier than drawing a diagram?
Example #2: The next morning you have 2 pairs of paints, 2 shirts, and three pairs of shoes to choose
from to make an outfit. How many different outfits could you arrange?
Example #3: An ID number to log in to a website must consist of 4 numbers followed by one letter.
Numbers are allowed to be repeated. How many different combinations are possible?
Step 1: Draw out blanks for your ID Number
_______ _______ _______ ________ ________
#
#
#
#
letter
Step 2: For blank #1, put the total number of possibilities in the blank. Do the same for all the other
blanks.
Step 3: Multiply all of these numbers together. This gives you the total number of possibilities for an ID
number on this website.
Example #4: Your license plate must consist of three letters followed by three numbers.
a) How many combinations are possible?
b) How many are possible if I do not want letters or numbers to repeat?
c) How many are possible if I do not want the letter O or the number 0 in my license plate?
d) How many license plates begin with 0 and end with A?
Example #5: How many different ways can 6 posters be arranged on the wall of our classroom?
Example #6: 2 women and 2 men will stand in line.
a) How many ways can they line up?
b) How many ways can they line up if the first person in line if a man?
c) How many ways can they line up in they alternate Man, Woman, Man, Woman?
Example #7:
a) How many different ways can the letters in the word DISCRETE be arranged?
b) How many ways can the letters in the word SENIORS be arranged is S must be in the first spot?