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permutations/combinations
dice
coins
cards
miscellaneous
100
How many ways can 5 students stand in a row?
120
100
What is the probability of rolling a die and having it land on a prime number?
1/2
100
If you flip a coin twice, what's the probability that they're both heads?
1/4
100
If you pick one cars from a standard deck at random, what is the probability of picking a jack or queen?
8/52 = 2/13
100
You flip a coin and roll a die. What's the probability of getting tails and a number greater than 3?
1/4
200
How many ways can a president and vice president be selected from a club of 8?
56
200
If you roll a dice twice, what is the probability that it lands on a 3 the first time and on an even number the second time?
1/12
200
If you flip two coins, what is the probability that they are different?
1/2
200
If you pick a card from a standard deck and put it back and then choose another one, what's the probability that the first one is a 9 and the second is a diamond?
4/52 x 13/52 = 52/2704 = 1/52
200
You spin a spinner that has 8 sections labeled 1-8. What is the probability that the spinner lands on an odd number or a number less than 5?
4/8 + 4/8 - 2/8 = 6/8 = 3/4
300
How many ways can 3 children out of 12 children be chosen to go in a car?
220
300
If you roll one die, what's the probability of rolling an even number or a prime number?
5/6
300
If you flip a coin 3 times, what is the probability that the first two are heads and the third is tails?
1/8
300
You randomly pick a card out of a standard deck. What is the probability that it is a black card or a king?
26/52 + 4/52 - 2/52 = 28/52 = 7/13
300
If 1/4 of the population has a cat 1/3 of the population has a dog, and 1/6 has both, what is the probability of randomly picking someone who has a dog or a cat?
1/4 + 1/3 - 1/6 = 5/12
400
You are choosing ice cream flavors to go in a sundae. If there are 8 flavors to choose from and you want 3, how many choices are there?
56
400
If you roll two dice, what is the probability that one is an odd number and the other is a number greater than 4?
1/6
400
If you flip a coin 3 times, what is the probability that all of them are the same?
1/4
400
You randomly pick a card from a standard deck and then choose another one without replacing it. What is the probability that they are both diamonds?
13/52 x 12/51 = 156/2652 = 1/17
400
A basketball player has a 74% success rate for free throws. If he has 2 free throws, what is the probability that he misses the first one but makes the second one?
.26 x .74 = 19.24%
500
A lock has 3 numbers 0-9 on it. If you know that the last number is odd and that the numbers can repeat, how many different lock combinations are there?
500
500
If you roll two dice, what is the probability that they are the same number?
1/6
500
If you flip 3 coins, what is the probability that 2 are heads and 1 is tails?
3/8
500
How many different 5-card poker hands are possible from a standard deck of cards?
2,598,960
500
You randomly pick a card out of a standard deck and without replacing it, pick another card. You then put both cards back in the deck, shuffle the deck, and choose a third card. What's the probability that the first two are both diamonds and the third is a king? Simplify completely.
13/52 x 12/51 x 4/52 = 1/221