Recurrence Relations
Multiplication Principle
Combinations & Permutations I
Combinations & Permutations II
Inclusion
100
Fill in the missing number. 21, 17, 13, ________, …
9
100
Solve for x. 15x – 42 = 3
x=3
100
How many different groups of four can be made from a class of 20 students?
20c4 = 4845 groups
100
Find the number of ways to rearrange the letters of ONOMATOPOEIA
12!/(4!*2!)
100
Out of 100 students, 35 are taking art and 60 are taking gym. How many students are taking neither?
5 students
200
Given the sequence 3n + 3, what is the 10th term?
33
200
If I cut two pizzas into eight slices each. How many slices do I have total?
16 slices
200
Your favorite store is having a sale! You can pick 3 shirts from 10 options, and 2 pairs of pants from 7 options. How many different outfits can you buy?
(10c3)(7c2) = 2520 outfits
200
You're putting pictures onto your computer from your last vacation in California. You have 27 in San Francisco, 49 in San Diego, and 16 in LA. How many different ways can you organize the pictures while still keeping the all the pictures from one spot next to each other?
(27! 16! 49!) 6!
200
Katie made 10 tie-dye shirts for her family. She counts 7 with blue and 8 with red. How many did she double count?
5 t-shirts
300
Given the sequence 4(n - 1) +6(n - 2) +3, what is the 4th term?
27
300
How many ways can you arrange the letters A, B, and C?
6 ways
300
How many seven digit phone numbers exist which do not repeat digits?
10c7 phone numbers
300
You have 25 fliers to put up for the school bulletin board. There are 6 math club, 2 football, 2 swimming, 8 reading club, 1 student council and 1 soccer. How many different ways can you put the fliers up?
25!/ (6! 8! 2!)
300
For mock elections, 32 students are nominated for best dressed and 29 are nominated for best smile. There are 14 students who are nominated for both. How many students were nominated for just best dressed and just best smile?
18 best dressed, 15 best smile
400
What is the relation for this sequence? 1, 2, 4, 8, …
2^n
400
My password for my email is 5 characters long. The password starts with 4581_____. How options are there for this last character, if the last character is a letter?
26
400
You and 3 of your friends are waiting in line for the movies. How many different ways can you and your friends stand in a line?
4*3*2*1= 24 ways
400
How many passwords can be made using 5 distinct letters?
26c5
400
Of your friends, 16 have an iPhone and 22 have an iPod. Actually, 9 of your friends have both. How many have just one of the items?
7 iPhone and 13 iPod
500
Find another t for which t satisfies the recurrence relation .
3
500
If I want chocolate, vanilla, superman, and moose tracks on one ice cream cone, how many ways can I order these 4 flavors?
24 ways
500
You have five different posters but you only have enough room for three in your room. How many different arrangements are possible?
5*4*3= 60 arrangements
500
How many different passwords can you make if the password must contain 6 letters and 2 numbers?
(26c6)(10c2)8!
500
Brian has a bag full of stickers that are a mix of orange, pink, and green. He counts 3 pink, 7 orange, and 8 green but he has only 13 stickers total. What is a possible way the stickers are colored?
5 orange and green, 3 pink, 2 orange, and 3 green
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