Probability, Counting & Combinatorics

This season, each team in the Davis City softball league will play each other team exactly once. If a total of 15 games will be played, how many teams are in the league?

The mayor’s two daughters each play for a different team in the Davis City softball league. This season, the mayor’s schedule will allow him to attend only one softball game. If he randomly selects which one of the 15 games to attend, what is the probability that the mayor will select a game in which at least one of his daughters is playing? Express your answer as a common fraction.

Here are a few of the problems that competitors had to solve as they faced off in head-to-head matches during the 2018 State Countdown Round.

Troy, Elliott and Shaun are three contestants on a game show. In one of the rounds of the game show the 3 contestants have a chance to spin a wheel up to two times in a row to try to get the highest possible sum without going over 100. The wheel that they spin is divided into 21 equal portions, each containing one element from the set of numbers containing 1 and all the multiples of 5 less than or equal to 100.

2017 School Sprint #29

Each year Desmond and his family take part in the cultural celebration of Kwanzaa. The observance centers around the seven principles of Kwanzaa: Umoja, Kujichagulia, Ujima, Ujamaa, Nia, Kuumba and Imani. Suppose Desmond writes each of the five letters of the seventh principle, Imani (Swahili for Faith) on its own index card. If Desmond places the five cards in a bag and randomly chooses three cards, what is the probability that he chooses the three letters of the fifth principle, Nia (Swahili for Purpose)? Express your answer as a common fraction.

Mrs. Hillestad has planned a dinner for 15 people this Thanksgiving. She bought 22.5 lbs of turkey, plus potatoes, cranberry salad, rolls and all of the traditional holiday food. Unfortunately, her daughter forgot to tell her that she was bringing three of her friends.  If Mrs. Hillestad wants to feed each person the same amount of turkey that she had originally planned, how much additional turkey must she purchase to accommodate these additional guests? Express your answer as a decimal to the nearest tenth.

The letters of the words GHOST, GHOUL, TRICK, TREAT and CANDY were written on 25 index cards, one letter per card. If the cards are shuffled and one card is selected at random, what is the probability that the card contains one of the letters in the word GHOST? Express your answer as a common fraction.

Kaleb has a bag containing red, black and white LEGO^® bricks. If he has 12 more red bricks than white bricks and 15 fewer white bricks than black bricks, what is the positive difference between the number of red bricks and black bricks in Kaleb’s bag?

Mrs. Marble refers to the three students named Ashley in her 3rd period gym class as Ashley G., Ashley E. and Ashley V. Mrs. Marble needs to divide the class to make 6 teams of 5 players for the dodge ball tournament. Each student has been assigned a number from 1 to 30. Mrs. Marble has placed 30 cards, each containing a number from 1 to 30, in a bowl. She will randomly select groups of 5 cards, without replacement to make the teams. What is the probability that all three Ashleys will be on the same team? Express your answer as a common fraction.