PRETTY PERMUTATIONS
What is 7 P 3?
210
What is 8 C 5?
56
How many ways can five books be arranged on a book shelf that has space for exactly five books?
120
Our math league has one team in the state of Pennsylvania. If a letter is chosen at random from the word PENNSYLVANIA, then what is the probability that it is the letter "N?" Express your answer as a common fraction.
1/4
If a fair coin is flipped six times, what is the probability that the result is four or more heads? Express your answer as a percent, rounded to the nearest whole percent.
34%
How many different words can I make rearranging the letters of APPLE?
60
How many ways can I pick two scarves to take with me on my trip to Iceland out of my collection of fifteen?
210
Order matters in what type of combinatorics problem?
combinations
Priyanka bought a bag of multi-colored organic carrots. Ten were yellow, seven were purple, five were red, and six were orange. If Priyanka chose a carrot at random, what is the probability that it was purple? Express your answer as a common (simplified) fraction.
1/4
What is the probability that, in a five-child family, there are at least two girls? Assume that the probability of a girl or a boy being born is the same. Express your answer as a common fraction.
13/16
How many ways can I award three prizes of different cash amounts to a class of 16 students?
3360
Twenty students signed up for a weekend ski trip, but only 16 students can go. How many ways can 16 of the 20 students be chosen to go on the ski trip?
4845
Of the 4 Edison brothers (Groucho, Chico, Harpo, and Zeppo), one will go to visit the zoo, one will visit the aquarium, one will visit grandpa, and one will stay home. How many different combinations of who-goes-where are there?
24
Two cubical dice, with faces numbered 1, 2, 3, 4, 5, and 6 are rolled. What is the probability that the sum of the numbers showing on the top surfaces of the two dice is greater than four? Express your answer as a common (simplified) fraction
5/6
Jocelyn has a bag of fruit chews containing the following flavors: 6 raspberry, 4 cherry, and 5 melon. If she chooses two at random, then what is the probability that they are the same flavor? Express your answer as a common fraction.
31/105
12-0
Twelve points are placed on the circumference of a circle. Three points are chosen randomly and connected to form a triangle. What is the maximum number of triangles that can be drawn?
12C3 = 220
A restaurant lets children build their own ice-cream sundae: They can select 2 scoops of ice-cream from a variety of 4 flavors, they can decide whether to add syrup and/or whipped cream, and have the whole thing served in a cup or a cone. How many different sundaes can be made?
80
Rolling a fair six-sided die times, what is the probability you never get a ‘6’? Express you answer as a percent, rounded to the nearest whole percentage.
33%
A bag of colored candy worms contains eight red, eleven green, and five blue eggs. Ella selects three worms at random and eats each one after selecting it from the bag. What is the probability that the three worms are the same color? Express your answer as a decimal, rounded to the nearest thousandth.
0.114
How many different 9-letter "words," or arrangements of letters, can be made by using the letters in the name RAMANUJAN ?
30,240
31 C 14 is the same as 31 C what number?
17
A piano teacher must choose four of her six seventh graders and five of her seven eighth graders to perform in a piano recital. She must then determine the order in which these nine students will perform. If the seventh graders! must all perform before any of the eighth graders, how many possible orders are there for the recital program?
907, 200
A six-sided cubical die, numbered 1 through 6 inclusive, and a ten-sided decahedral die, numbered 1 through 10 inclusive, are rolled. What is the probability that the sum of the numbers shown on the top faces is less than 8 ? Express your answer as a common fraction.
7/20
Jihoon flipped a coin 8 times in a row. If it is known that he did not flip two consecutive heads, what is the probability that he flipped exactly 3 heads?Express your answer as a common!fraction
4/11