Factorials
This is the result of 3!
What is 6? (3 x 2 x 1)
If you have 3 shirts and 5 pants, this is the number of different outfits you can make.
What is 15? (3 x 5)
This counting method is used when order matters, like arranging items on a shelf.
What is a permutation?
This counting method is used when order does NOT matter, like choosing toppings for a pizza.
What is a combination?
How many different ways can the letters in the word "CAT" be arranged?
What is 6? (3! = 3 x 2 x 1)
This is the value of 6!
What is 720? (6 x 5 x 4 x 3 x 2 x 1)
If a password must have 2 letters (A-Z) followed by 1 digit (0-9), this is the total number of passwords possible. (Repetition is allowed).
What is 6,760? (26 x 26 x 10)
This is the number of ways to arrange all 4 different textbooks on a shelf.
What is 24? (4 x 3 x 2 x 1)
This is the number of ways to choose 2 friends to go to the movies from a group of 5 friends.
What is 10?
C(5,2) =
(5x4)/(2 x 1)
How many ways can you choose 2 scoops of ice cream from 8 flavors if order doesn't matter?
What is 28?
C(8,2) =
(8x7)/(2x1)
Rewrite the calculation 10 x 9 x 8 using factorials.
What is
(10!)/(7!)
A coin is flipped 4 times. This is the number of possible sequences of heads and tails.
What is 16? (2 x 2 x 2 x 2)
This is the number of ways 6 students can finish a race in 1st, 2nd, and 3rd place.
What is 120? (P(6, 3) = 6 x 5 x 4
This is the number of different 3-person committees that can be selected from a club of 7 members.
What is 35?
C(7,3) =
(7 x 6 x 5)/(3x2x1)
You are trying to find all the different possible combinations for the last 4 digits (0-9) of a phone number. How many 4-digit numbers are possible if repetition is allowed?
What is 10,000? (10 x 10 x 10 x 10)
Simplify the expression
(10!)/(9!)
What is 10?
A menu has 4 appetizers, 8 main courses, and 3 desserts. This is the number of ways to order a three-course meal.
What is 96? (4 x 8 x 3)
This is the number of ways to pick a specific captain and a specific co-captain from a team of 10 people.
What is 90? (P(10, 2) = 10 x 9)
A baker offers 12 types of muffins. This is the number of ways a customer can choose a box of 4 different muffins.
What is 495?
C(12,4) =
(12x11x10x9)/(4x3x2x1)
How many different ways can 4 students sit in 6 available seats?
What is 360?
P(6,4) = 6 x 5 x 4 x 3
Simplify the expression
(n!)/((n-1)!)
What is n?
A three-digit number is formed using the digits 1, 2, 3, 4, 5. If repetition is allowed, this is the number of different three-digit numbers possible.
What is 125? (5 x 5 x 5)
How many distinct arrangements can be made from the letters of the word MISSISSIPPI such that the four I's are never all together?
33,810 ways
A school's basketball coach needs to select a starting lineup of 5 players from a pool of 12 candidates.
The 12 candidates consist of 5 guards & 7 forwards.
The coach must follow these constraints:
The lineup must include at least 3 Guards.
The lineup must include at most 3 Forwards.
How many different starting lineups can the coach choose?
What is 246 different starting lineups?
How many distinct arrangements of the letters in the word 'COMPUTER' are possible if all the vowels (O, U, and E) must always stay together?
What is 4,320?
Treat the 3 vowels as a single "block" of letters. The new word has the letters CMPTR and 'OUE' which has 6 distinct units. The 6 units can be rearranged 6! ways and the vowels within the block can be rearranged 3! ways. 6! * 3! = 720 * 6 = 4,320 ways