Multiplication Principle

Piece of cake

200

You lose half of you're points!!!!

OH NOOO!!!Why did you chose that!!!

400

A license plate consists of:

• 2 letters (A-Z)
• 3 digits (0-9)
• Cannot have repeated letters
• Cannot have repeated digits

How many different license plates can be created?

26×25×10×9×8=468,000

600

You just stole the turn so pick another question! You also win the question points

Great Luck 🍀 🍀 🍀 🍀 🍀 

800

A 4-digit PIN is made from 0-9, but digits cannot repeat:

• First digit → 10 choices (0-9)
• Second digit → 9 choices (can’t be the first digit)
• Third digit → 8 choices
• Fourth digit → 7 choices

Total PINs:

10×9×8×7=5,040

1000

• If a password consists of 2 letters followed by 3 digits, and:

• a)Each letter can be any of 26 letters

• b) Each digit can be any of 10 digits

• How many passwords can u make?
  
  
  

676,000 paswords

Pretty Easy

200

An ice cream shop lets you choose:

• 3 flavors (Chocolate, Vanilla, Strawberry)
• 2 types of cones (Waffle, Sugar)
• How many different ice cream choices do you have?

 you can chose 6 different ice cream combinations! 🍦

400

If you have 3 shirts (Red, Blue, Green) and 2 pairs of pants (Jeans, Black), how many different outfits can you make?

2x3=6 so 6 different outfits

600

You can switch you're points with another group or take only 200 points from another team! you also win these points!

Great choice🍀 🍀 🍀 🍀 🍀 

800

A company generates 5-letter security codes, where:

• The first letter must be a vowel (A, E, I, O, U) → 5 choices
• The next four letters can be any letter from A to Z → 26 choices per letter
• How many different security codes can u make?

5×26×26×26×26=2,284,880 security codes can be made

1000

A security code consists of:

• 3 uppercase letters (A-Z, 26 choices each)
• 1 digit (0-9, 10 choices)
• how many security codes can you form?

26×26×26×10=175,760 type of different security codes

Very Very Easy

200

A sandwich shop lets you pick:

• 4 types of bread
• 5 types of fillings

How many different sandwiches can you make?

You can have 20 different sandwiches! 🥪

400

A person wants to travel from City A to City C with a stop in City B.

• There are 5 different flights from A to B.
• There are 4 different flights from B to C.
•  how many ways are there to travel from City A to City C.

5x4=20 there are 20 ways to travel from City A to City C. 

600

A student must pick one subject from each category:

• 3 science subjects (Biology, Chemistry, Physics)
• 4 math subjects (Algebra, Geometry, Trigonometry, Calculus)
• 2 history subjects (Ancient, Modern)
• How many schedules can the student make?

3x4x2=24 so the student can make 24 different schedules.

800

In a group of 6 students, 2 must stand next to each other.

• First, treat the 2 students as a single "super-student" 
• Inside their "super-group," the 2 students can switch places:

5!=120 and 2!=2 then 120×2=240 

There could be 240 ways so that the student group can be arranged.

1000

A group of 7 people (A, B, C, D, E, F, G) needs to sit in a row.
However, A and B must always sit together and C and D must also sit together.

How many different ways can they be arranged?

5!×2!×2!=120×2×2=480

Getting Harder

200

A security code consists of 3 digits, where:

• The first digit can be any number from 1 to 9 (9 choices, no 0).
• The second and third digits can be any number from 0 to 9 (10 choices each).

How many different security codes can be made?

There are 900 different security codes possible!

400

YOU have the ability to take half of the other team points!!!! you also win these points!

Which one will you chose???🍀 🍀 🍀 🍀 

600

A 5-character password consists of:

• First character must be a number (0-9) → 10 choices
• Second character must be a letter (A-Z) → 26 choices
• Last three characters must be digits (0-9) → 10 choices each

Total passwords:

10×26×10×10×10=260,000

800

A 4-letter code is created using:

• The first letter must be a vowel (A, E, I, O, U) → 5 choices
• The next 3 letters can be any letter from A-Z → 26 choices each

How many different codes can be made?

878,080 4-letter code can be created.

1000

A 6-character password consists of:

• The first character must be a digit (0-9) → 10 choices
• The second and third characters must be uppercase letters (A-Z) → 26 choices each
• The last three characters must be lowercase letters (a-z) → 26 choices each

10×26×26×26×26×26=118,813,760 

there are 118,813,760 possible passwords

Extremely Hard

200

A pizza place lets you choose:

• 3 types of crusts (Thin, Regular, Deep Dish)
• 5 types of toppings (Pepperoni, Mushrooms, Onions, Peppers, Olives)
• 2 types of sauces (Tomato, Alfredo)
• How many different pizzas can be made?

You can create 30 different pizzas with these options! 🍕

400

A 4-digit lock has numbers 0-9, but the first digit cannot be 0:

• First digit: 9 choices (1-9)
• Other three digits: 10 choices each

Total combinations:

9×10×10×10=9,000

600

A family of 5 people (A, B, C, D, E) wants to sit in a row.

• How many ways can they sit?

5!=5×4×3×2×1=120 

They can sit in 120 ways

800

A license plate has:

• 2 letters (A-Z, 26 choices each)
• 3 digits (0-9, 10 choices each)
• Ends with 1 letter (A-Z, 26 choices)
• Tell me the Total plates?

17,576,000 is the total number of plates

1000

You have 7 different books, but:

• 3 of them are math books that must be kept together.
• The other 4 books (science, history, etc.) can be arranged freely.

How many ways can you arrange all 7 books on a shelf?

5!×3!=120×6=720 

1. Grouping Rule: When some objects must stay together, we treat them as a single "super-object."
2. Multiplication Principle: Since arranging the grouped books and arranging the inside books are independent steps, we multiply the possibilities.