Passwords and Fundamental Counting Principle

Which of the following situations is represented by this tree diagram?

• 3 shirt options, 6 pants options, and 12 shoe options
• 3 shirt options, 2 pants options, and 2 shoe options
• 2 shirt options, 3 pants options, and 1 shoe option
• I'm really not sure

How many possible combinations of outfits could one make if they had to choose one shirt, one pair of pants and one kind of footwear?

• 12

• 21

• 7

• 3

• I'm really not sure

How many styles of sneakers are possible if Jared can choose from high-top or low-top, shoelaces or velcro, and the colors black, white, and red?

• $2\times2\times3=12$

• $2+2+3=7$ 7

• two choices, two choices, three choices = $223$
  

• $\left(2+2\right)^3=64$
  

How many different passwords could you make if you could use 3 digits?

• 100
• 1000
• 10000
• 100000
• I'm really not sure

How many possible outcomes are there if you flip 4 coins?

• 8
• 16
• 4
• 12
• I'm really not sure

How many unique license plates could you make if you had to use 2 digits followed by 3 letters?

• 676000
• 1757600
• 67600
• 17576
• I'm really not sure

How many passwords could you make if you had to use 8 letters?

• 208 billion
• 208 million
• 208 trillion
• 208 thousand
• I'm not really sure

How many passwords could you make if you could use 8 letters (either uppercase or lowercase)?

• 208 billion

• 4 billion

• 26 million

• 53 trillion

• I'm not really sure

A password must be two digits followed by three letters. If repeats of symbols ARE allowed, how many passwords are possible?

• 10 X 9 X 26 X 25 X 24

• 10 X 10 X 26 X 26 X 26

• 10 + 10 + 26 + 26 + 26

• 10 + 9 + 26 + 25 + 24

• I'm really not sure

How many unique passwords could you make if you used 12 letters that could be either uppercase letters or lowercase letters or digits?

• 62^12
• 36^12
• 72^12
• 52^12
• I'm really not sure