Decisions, Decisions
How many ways can 10 people wait in line for tickets?
10! or 3,628,800 ways
How many ways can 5 paintings be lined-up on a wall?
5! or 120 ways
How many ways can the letters IDAHO be arranged?
5! = 120 ways
An ice cream shop offers 8 different flavors, 10 different toppings, and the choice between a cake cone, waffle cone, or a dish.
If I wanted a single scoop with one topping, how many different treats could I make?
(8 x 10 x 3) = 240 treats
Captain America is putting together a small team of four heroes to help him with a mission. If he has seven recruits to choose from, how many ways can he pick his team?
(7 x 6 x 5 x 4) / 4! = 35 ways
Rob has 4 shirts, 3 pairs of pants, and 6 pairs of shoes that all coordinate. How many outfits can be put together?
(4 x 3 x 6) = 72 outfits
Four students are to be chosen from a group of 10 to organize the Winterfest Dance. How many ways can this group of 4 be made?
(10 x 9 x 8 x 7)/(4!) = 210 ways
How many ways can the letters OHIO be arranged?
(4!)/(2!) = 12 ways
If an ice cream shops offers 8 different flavors, how many ways can I get a treat with 3 scoops of any flavor?
(8 x 8 x 8) = 512 ways
Assuming he could've obtained them in any order, how many different ways could Thanos have obtained the six infinity stones?
6! = 720 ways
Your social security number is 9 digits long and use the numbers 1 through 9. How many social security numbers are possible?
(9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9) = 387,420,489 Social Security numbers
In math class, there are 24 students. The teacher picks 4 students to help do a demonstration. How many different groups of 4 could she have chosen?
(24 x 23 x 22 x 21) / 4! = 10,626 groups
How many ways can the letters ALABAMA be arranged?
(7!)/(4!) = 210 ways
An ice cream shops offers 8 different flavors. Assuming you eat ice cream cones from the top down (in order), how many ways can I get a cone with 3 scoops, each one a different flavor?
(8 x 7 x 6) = 336 ways
Tony Stark has 52 versions of his Iron Man armor. Pepper Potts convinces him to place them into storage, but Tony decides he wants to keep one on remote standby, another one at his house, one in his car, and another in his private jet. How many ways can he choose those four Iron Man suits?
(52 x 51 x 50 x 49) = 6,497,400 ways
A Wisconsin license plate typically contains 3 letters followed by 3 digits. How many different license plates are possible?
(26 x 26 x 26 x 10 x 10 x 10) = 17,576,000 plates
Four students are to be chosen from a group of 10 to fill the positions of president, vice-president, treasurer, and secretary. How many ways can those positions be filled?
(10 x 9 x 8 x 7) = 5,040 ways
How many ways can the letters WISCONSIN be arranged?
(9!)/(2! 2! 2!) = 45,360 ways
An ice cream shop offers 8 different flavors, 10 different toppings, and the choice between a cake cone, waffle cone, or a dish.
If I wanted a single scoop with two different toppings, how many different treats could I make?
(8 x ((10 x 9)/2!) x 3) = 1080 treats
Hawkeye has 15 normal arrows, 7 taser arrows, 1 grappling arrow, and 12 grenade arrows in his quiver. If he knows which arrows he is selecting, how many ways can he fire the first three arrows, considering the first two are neither a taser arrow nor the grappling arrow?
(27 x 26 x 33) = 23,166 ways
A lock manufacturer uses a spinning dial, with the numbers 0 through 30, as part of the combo lock. How many three-number combos for the lock are possible?
(31 x 31 x 31) = 29,791 combinations
Your teacher has listed 30 books as a book report options. You must read 2 books and create a report for each. How many different sets of 2 books could you have chosen to read?
(30 x 29) / 2! = 435 ways
How many ways can the letters MISSISSIPPI be arranged?
(11!)/(4! 4! 2!) = 34,650 ways
An ice cream shop offers 8 different flavors and 10 different toppings. Assuming I can eat the ice cream in a dish in any order, how many different dishes could I make with three different flavors of ice cream and two different toppings?
((8 x 7 x 6) / 3!) x ((10 x 9) / 2!) = 2520 treats
Peter Parker forgot the five digit passcode to the Avengers Tower. He remembered that every digit was different, the first digit was 0, and the third digit was an even number. How many total passwords would he have to guess?
(1 x 8 x 4 x 7 x 6) = 1,344 ways