Permutations and Combinations
A track and field team has 5 members. How many ways can the coach organize a 5-person relay team?
120
5! multiplication principle or
nPr (5!)/(5-5)!
26/52 or 50%
You draw a card from a standard deck of cards. What is the probability that the card is either the Queen of Hearts or the Ace of Spades?
2/52 or 3.8%
(1/52 + 1/52)
What is the probability a randomly selected student is a senior or in the band?
108/186 or 58.1%
How many 4 person committees can be formed from 10 city council members?
210
nCr = (10!)/(10-4)!(4!)
The local weather forecast has been accurate for 14 of the past 23 days. Based on this fact, what is the probability that the forecast for tomorrow will be correct?
14/23 or 60.9%
You draw a card from a standard deck of cards. What is the probability the card is either a 7 or a diamond?
16/52 or 30.8%
(4 sevens + 13 diamonds - 1 seven of diamonds)
(see 2-way table)
What is the probability that a randomly selected student is a sophomore and a theatre kid?
23/186 or 12.4%
A corporation has 15 members on its board of directors. How many ways can it elect a president, vice-president, secretary, and treasurer?
32,760
nPr = (15!)/(15-4)!
You have a standard deck of cards. What is the probability that a randomly selected card will be odd (3, 5, 7, 9) or a spade?
(16 odd cards + 13 spades - 4 odd spades)
An aquarium has 26 African penguins (15 males and 11 females) and 13 rockhopper penguins (6 males and 7 females). What is the probability that a randomly chosen penguin is a female or an African penguin?
33/39 or 84.6%
(18 females + 26 African penguins - 11 female African penguins)
(see 2-way table)
What is the probability a student is a junior, given that they play in the orchestra?
19/44 or 43.2%
How many 5-digit ZIP codes can be made with the digits 0-9?
100,000
10*10*10*10*10 Multiplication principle
1/8 or 12.5%
Use the table for exercise 11.19 in your notes.
What is the probability any randomly selected driver is an adult and has 0 or 1 accidents?
85/125 or 68%
(see 2-way table)
What is the probability that a student plays an instrument, given that they are a sophomore?
25/48 or 52.1%
A lottery ticket requires players to select 5 distinct numbers from 00 to 99 to appear on the ticket. How many unique tickets are possible?
75,287,520
nCr = (100!)/(100-5)!(5!)
A bag of balls contains 3 yellow balls, 6 red balls, and 4 green balls. I reached in and grabbed a red ball and did NOT put it back. What is the probability you are going to randomly grab another red ball?
5/12 or 41.7%
Out of 150 students in a senior class, 98 students are either varsity athletes or on the honor roll. There are 68 seniors who are varsity athletes and 47 seniors who are on the honor roll. What is the probability that a randomly selected senior is both a varsity athlete and on the honor roll?
17/150 or 11.3%
(see 2-way table)
What is the probability that a student is a junior or a senior, given that they are in the band or do theatre?
102/142 or 71.8%