# Probability, Counting & Combinatorics

## St. Patrick's Day

Riley sees a rainbow with ends that appear to touch the ground 1 mile apart and reaches a maximum height of 0.5 miles above the ground. If the rainbow is an arc of a circle, how many degrees is the arc that Riley sees?

*First, let's draw a diagram: *

## Iditarod

*The Iditarod sled-dog race is run on a trail that was originally a mail-supply route. In 1925, part of the trail became a lifesaving highway for the children who lived in Nome.*

*The Iditarod is sometimes called “The Last Great Race on Earth.” Every year, it begins in Anchorage, Alaska during the first weekend in March. Each team of 12 to 16 dogs and a musher covers the distance to Nome in approximately 9 to 20 days.*

## State Competitions

*State Competitions are coming up fast! Are you ready to compete? Let’s try a few 2019 State Competition problems to get ready.*

__2019 State Sprint Round, #18__

If C is a digit such that the product of the three-digit numbers 2C8 and 3C1 is the five-digit number 90C58, what is the value of C?

## Valentine's Day Treats

According to “A History of Valentine’s Day Cards in America” by T.M. Wilson, in 1847 Esther Howland was the first to mass-produce Valentine’s Day cards. She made them out of lace, paint and expensive paper and each one was individually written by a skilled calligrapher. The average card sold for $7.50 while others cost as much as $50. If 10 cents in 1847 would be equivalent to $1.85 today, how much would the average card and most expensive card have cost today?

## Let the Competitions Begin!

Chapter Competitions officially started this past weekend! Are you ready to compete? Let’s try a few 2019 Chapter Competition problems to get warmed up.

__2019 Chapter Sprint Round, #20__

Jones is chasing a car 800 meters ahead of him. He is on a horse moving at 50 km/h. If Jones catches up to the car in 4 minutes, how fast was the car moving?

*Jones catches up 800 m in 4 min and thus, at a rate of:*

## MATHCOUNTS Competition Season Approaches

The Sprint Round of the MATHCOUNTS Chapter Competition has 30 questions and students are given 40 minutes to complete the round. Though it isn’t expected that most students will finish all 40 questions, what is the average time a student can spend on each of the 30 questions, in minutes:seconds per question?

## I Have a Dream!

*The third Monday of January is the holiday commemorating the birthday of Martin Luther King, Jr. The first time Martin Luther King Jr. Day was celebrated was in 1986. Try to solve these problems without using a calendar!*

How many times has Martin Luther King Jr. Day been celebrated?

## Eight is Enough!

In 1998, Nkem Chukwu gave birth to the first set of surviving octuplets. The eight babies weighed from 11.3 ounces to 28.6 ounces at birth. Leonard Weisman, the Texas Children’s Hospital’s chief of neonatal services, said it was imperative they gain lots of weight before they go home. “For instance, the 500-gram babies are going to have to quadruple their weight [to reach a healthy level],” he said. How many ounces will the heaviest baby have to gain to reach a healthy level?

## Best of 2019!

*While there were many problems written and solved for MATHCOUNTS in 2019, below is a selection of some of the best of the year! *

__2018-2019 School Handbook, #27__

A segment with endpoints G(-2, 3) and H(4, 7) is dilated by a scale factor of 2/3 with center of dilation (0, 0). What is the sum of all the coordinates of G’ and H’?

## Hayride

Abby, Brenda, Celia, Denise and Elizabeth are going to their town’s annual hayride. Tickets cost $8.00 for people 12 years old and older but only $5.00 for people 11 years old and younger. The total price for their five tickets is $31.00. How many people in the group are 12 years old or older?