Permutations & Combinations
You have 6 different books. How many ways can you arrange all of them on a single shelf?
720
(6!)
A bag contains 4 red, 5 blue, and 3 green marbles. What is the probability of drawing a blue marble?
5/12
A card is drawn from a standard deck. What is the probability that the card is a 7 or a Diamond?
16/52 or 4/13
A box contains 5 red and 3 blue balls. Two balls are drawn at random without replacement. What is the probability that both are red?
5/14
(C(5,2)/C(8,2) or 5/8*4/7)
A single die is rolled. What is the probability the result is a 6, given that the result is an even number?
1/3
From a group of 10 students, how many ways can a committee of 3 be chosen?
120
(C(10,3))
A single die is rolled. What is the probability of NOT rolling a 2?
5/6
You flip a coin and roll a die. What is the probability you get Heads and a 5?
1/12
(1/2 * 1/6)
A coin is flipped three times. What is the probability of getting exactly two heads?
3/8
(C(3,2)/28)
In a class, 50% are freshmen and 20% are freshmen who are also business majors. What is the probability that a randomly selected freshman is a business major?
0.4 or 40%
(0.2 / 0.5)
In how many distinct ways can the letters of the word BALLOON be arranged?
1260
(7! / 2!2!)
Two coins are flipped. What is the probability of getting at least one Head?
3/4
What is the probability of rolling a 1 OR a 6 on a single die roll?
2/6 or 1/3
A committee of 3 people is chosen at random from 4 men and 2 women. What is the probability the committee has exactly 2 men and 1 woman?
3/5
(C(4,2)×C(2,1))/C(6,3)
Two fair dice are rolled. Given their sum is 8, what is the probability at least one die shows a 3?
2/5
A committee of 4 people is to be formed from a group of 6 men and 7 women. How many committees can be formed if the committee must have exactly 2 men and 2 women?
315
(C(6,2) * C(7,2))
From a standard 52-card deck, what is the probability of drawing a card that is red and is also a face card (J, Q, K)?
6/52 or 3/26
At a university, 50% of students take a math class and 60% take an English class. If 30% of students take both, what is the probability that a randomly selected student takes math or English?
80% or 0.8
A 5-card hand is dealt from a standard 52-card deck. What is the probability that all 5 cards are from the same suit?
0.00198
4 * C(13,5)/C(52,5)
From a standard 52-card deck, this is the probability of drawing a King OR a Heart, given that the card drawn is a Face Card (a King, Queen, or Jack).
1/2
You are planning a party and have a list of 6 friends you are thinking of inviting. You can invite any number of them. How many different combinations of guests could you invite?
64
(2^6)
You roll two standard six-sided dice. What is the probability that the sum of the numbers rolled is less than 5?
6/36 or 1/6
What is the probability of drawing a King OR a Club from a standard deck of 52 cards?
16/52 or 4/13
A password consists of 4 letters (A–Z) followed by 2 digits (0–9). What is the probability that a randomly chosen password has no repeated letters or digits?
(Round your answer to 3 decimals)
0.707
P(26,4)*P(10,2) / 26^4 * 10^2
At a university, 20% of all students are in the College of Science and live on-campus. 40% of all students are in the College of Arts and live on-campus. These are the only two colleges at the university. What is the probability that a randomly selected student who lives on-campus is in the College of Science.
1/3
0.20/(0.20+0.40)