Audrey has 5 dresses, 10 pairs of shoes and 13 headbands. She wants to try on every possible combination of dresses, headbands and shoes. How many combinations will she have to try?
650
100
There is a class of 80 students running for student council. Each slate that runs has a president, vice president, secretary and treasurer. How many possible slates are there that could run?
37,464,960 slates
100
How many ways can you choose a group of 4 students from a class of 12?
495
100
A scrabble bag has one of each letter in the alphabet left in the bag. How many different ways could you select 7 letters out of the bag, if the order in which you select the letters matters?
3,315,312,000
100
How many 5 digit numbers are there with no repeating digits?
27216
200
Alex has twice as many bracelets as she has rings. If she has n rings, then how many bracelet and ring combinations does she have?
2n^2
200
20 people are playing musical chairs. In a strange twist, 17 chairs are removed from the game at the end of the first round. How many different arrangements in the remaining chairs could there be? Order matters.
6840
200
How many ways are there to choose a group of 3 students from a class of 75 students?
67,525
200
New words can be made from mixing up the letters in the word SCRAMBLED. Repeated letters are allowed. What is the probability that a randomly selected word will contain all distinct letters?
362,880 / 387,420,489
200
How many even 5 digit numbers are there?
45000
300
I have a pile of 10 t-shirts on the floor of my bedroom, which I've procrastinated on putting away. To put them away, I must pick up one t-shirt at a time, fold it, and put it into the drawer. In how many different orders could I put the t-shirts away?
10!
300
On a secret ballot, there are 10 questions. The first 4 questions ask the voter to choose either a Democratic, Republican, or an Independent Candidate. The next three questions ask the voter to select from a list of 8 possible candidates for their local government. The last two questions ask the person to vote either Yes or No on an issue. How many possible ways are there to fill out this ballot?
597
300
There are 20 freshmen, 15 sophomores, 10 juniors and 5 seniors in Parksingers. For each individual class, how many possible pairs could be chosen?
The letters in the word FORGET can be used to make other 6 letter words. If the first letter and third letter must be a vowel, and letters cannot repeat, how many combinations for the 6 letter word could you make?
2*4!
300
How many 7-digit numbers are there that are divisible by 5?
1,800,000
400
Roni has a selection of 4 different green shirts and 5 different blue shirts. They also have a selection of 6 different yellow pairs of pants and 3 different pink pairs of pants. What is the probability that Roni will choose a green shirt and a yellow pair of pants?
24/81
400
There are 18 people running for office. There are 3 possible distinct seats to run for. How many different slates are possible?
4896
400
A group of 5 students lines up in a row. Each student has two initials. What is the chance of me going down the row and guessing, exactly, each of the students' initials?
1 / (1.411671*10^14)
400
The letters in the word FLORIDA can be scrambled to create other 7-letter words (no repeats). How many different 7-letter words can you make if the first and last letters MUST be vowels?
3*4!
400
You roll a 6-sided die 8 times. What is the probability that you will roll all even numbers?
6,561 / 1,679,616
500
Shay wants to wear a different outfit each day for the entire school year, which consists of 180 days. They have 5 hats, 3 pairs of shoes, and they have twice as many shirts as they have pairs of pants. What is the minimum number of pairs of pants Shay could own to make their dream come true?
3 pairs of pants
500
On a secret ballot, there are 15 questions. The first 5 ask voters to choose from 2 candidates (Democrat or Republican), the next 5 questions ask voters to select from 4 independent candidates, and the last 5 questions ask voters to vote Yes or No. How many ways can a voter who always votes for the Democrats on the ballot fill it out?
1056
500
How many different ways can a group of 10 students line up, if the first and last student are always assigned to be in those positions?
8!
500
An old license plate from Maryland contains three letters followed by a three-digit number (no leading zero). How many possible license plate combinations can there be if the 3 digit number must be even?
7,909,200
500
There are 4 Czech and 3 Slovak books on the bookshelf. Czech books should be placed on the left side of the bookshelf and Slovak books on the right side of the bookshelf. How many ways are there to arrange the books?