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Excel in math and science
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Combinations
If a coin is flipped twenty times, how many ways are there to get exactly ten tails and ten heads?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Concept Quizzes
A bakery sells three kinds of pastries: donuts, muffins, and cookies. If you go to the store to buy \(28\) pastries, how many different combinations of them can you buy if they only have \(27\) of each type available?
Details and assumptions
All the pastries of one type are indistinguishable.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
For his reverse birthday party, George is giving away bags with toys in them. If the party store sells 4 different toys and George is making \(9\) bags, each with a single toy in it, how many different combinations of toys can George make?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
How many ways are there to choose distinct numbers \(a, b\) and \(c\) from among the integers \(\{1, 2, \ldots, 110\}\) such that \(a+b+c\) is an even number?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Cards for a trading card game can be purchased in packages of 6 cards, of which exactly 1 of them is a rare card.
If there are a total of 8 rare cards that can be collected, and you purchase \(3\) packages of cards, how many different combinations of the rare cards could you end up with?
For example, you could have 1 of the second rare cards, and the rest are the eighth rare card.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
You have 6 identical balls and 6 (distinct) boxes numbered \(1\) through \(6.\) How many ways can the 6 balls be distributed amongst the boxes?
Details and assumptions
Some of the boxes can be empty.