Combinations
Permutations
Complementary
Mixed
Hard!! (500+ pts)
100
In how many ways can 5 students be selected from a group of 6 students?
6
100
My club has 15 members. In how many ways can we choose a president, vice-president, secretary, and treasurer, if either the secretary or the treasurer must be elected vice-president and no other member can hold more than one office?
5460
100
The planning committee at school has 10 members. Exactly four of these members are teachers. A four-person subcommittee with at least one member who is a teacher must be formed from the members of the planning committee. How many distinct subcommittees are possible?
195
100
A zoo has a menagerie containing four pairs of different animals, one male and one female for each. The zookeeper wishes to feed the animals in a specific pattern: each time he feeds a single animal, the next one he feeds must be a different gender. If he starts by feeding the male giraffe, how many ways can he feed all the animals?
144
100
Phillip flips an unfair coin eight times. This coin is twice as likely to come up heads as tails. How many times as likely is Phillip to get exactly three heads than exactly two heads?
4
200
A plane is uniquely determined by three non-collinear points. What is the maximum possible number of planes that can be determined by 12 points in space?
220
200
At the beginning of every period of British Literature, Mrs. Crabapple picks a random student to receive a crabapple as a gift, but really, as you might imagine, they are quite bitter and nasty. Given that there are 11 students in her class and her class meets four times a week, how many different sequences of crabapple recipients are possible in a week?
14641
200
If x% of four-digit numbers have a repeated digit (the repeated digits do not need to be adjacent), then what is x? Express your answer as a decimal to the nearest tenth.
10
200
Abe, Bobby, Charles, Devin and Edwin are the participants in a race. How many different 1st-2nd-3rd place outcomes are possible if there are no ties? Two different outcomes to include are Bobby-Devin-Edwin and Devin-Bobby-Edwin.
60
200
How many perfect square factors does the number 46,656 have?
16
300
Consider a regular octagon. How many triangles can be formed whose vertices are the vertices of the octagon?
56
300
A standard deck of cards has 26 cards which are considered "red" (the 'hearts' and 'diamonds') and 26 which are considered "black" (the 'spades' and 'clubs'). In how many different ways can we choose two red cards from the deck? (Note: Order matters in the sense that drawing an ace of hearts followed by jack of diamonds is different than drawing a jack of diamonds followed by ace of hearts, for instance.)
650
300
How many integers from 1 through 9999, inclusive, do not contain any of the digits 2, 3, 4 or 5?
1294
300
A teacher wants to arrange 3 copies of Introduction to Geometry and 4 copies of Introduction to Number Theory on a bookshelf. In how many ways can he do that?
35
300
How many solutions are there to a + b + c + d = 8, subject to the condition that each of the variables is a positive integer?
35
400
Our basketball team has 10 players. We need to divide into two teams of 5 for an intra-squad scrimmage. In how many ways can we do this without restrictions?
126
400
Elodie is putting on a fashion show and has five fabulous outfits for her five fabulous fashion models. However, on the day of the show, two of the outfits were ruined in an unfortunate permanent marker incident. Regardless, the show must go on and the remaining outfits will be presented. If each outfit can only be worn by one model and there is no time for any model to wear more than one dress, how many different shows can Elodie put on? (Note: Two shows are considered the same if they contain the same models wearing the same dresses.)
60
400
What is the probability that when tossing two dice, at least one dice will come up a "3"?
11/36
400
If {x,y} is a subset of S={1,2,3,....50}. What is the probability that xy is even?
Note to Disha: Remember to explain!
37/49
400
A parking lot has 16 spaces in a row. Twelve cars arrive, each of which requires one parking space, and their drivers chose spaces at random from among the available spaces. Auntie Em then arrives in her SUV, which requires 2 adjacent spaces. What is the probability that she is able to park?
17/28
500
Look at board
21
500
The positive five-digit integers that use each of the digits 1, 2, 3, 4 and 5 exactly once are ordered from least to greatest. What is the 50th integer in the list?
31254
500
Amy tosses a nickel four times. What is the probability that she gets at least as many heads as tails ?
11/16
500
A nursery employee wishes to plant 2 identical Golden Delicious apple trees and 5 identical Bartlett pear trees in one row. How many distinct arrangements are possible?
21
500
Many states use a sequence of three letters followed by a sequence of three digits as their standard license-plate pattern. Given that each three-letter three-digit arrangement is equally likely, the probability that such a license plate will contain at least one palindrome (a three-letter arrangement or a three-digit arrangement that reads the same left-to-right as it does right-to-left) is 
, where 
and 
are relatively prime positive integers. Find 
59