Counting Methods Basics

Question 1

When asked to count the total number of outcomes for a given event what are the two questions to ask yourself?

Answer 1

Are you drawing from one single source?

Or are you drawing from multiple sources?

Question 2

A space shuttle crew consists of one Commander, one Medical Officer, and One Chief Scientist. If there are 5 candidates for commander, 4 for medical officer and 3 for chief scientist, and no candidates applies for more than one position, how many different shuttle crews are possible?

Answer 2

Commander: 5 candidates
Medical Officer: 4 candidates
Chief scientist: 3 candidates

So to know how many different crews are possible you multiply 5 * 4 * 3 = 60

answer = 60

Question 3

Which part of counting problems should you solve first?

Answer 3

If there are any restrictions in place, solve the restrictions first

Question 4

Six children, one boy and five girls, must stand in line. If the boy cannot stand first or last in line, in how many different ways could the children be arranged?

720 
480 
360 
240 
120

Answer 4

Start by setting up one spot for each position in line (there are 6)

5 4
_ _ _ _ _ _
g g
^ by doing the restrictions first 5 people could stand first and 4 people could stand last (no boys and -1 girl) you can fill in the rest

5 * 4 * 3 * 2 * 1 * 4 = 480

Question 5

What is the primary operation for counting questions?

Answer 5

multiplication!

Question 6

What is the definition of a factorial?

n! = n * (n - 1) (n -2) (n - 3) .. until you get to 1

ex. what is 4! ?

Answer 6

4! = 4 * 3 * 3 * 1 
4! = 24

Question 7

what is 3! = ?

Answer 7

3! = 3 * 2 * 1

Question 8

what is 0! = ?

Answer 8

0! = 1