Six choices how many combinations

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There are 20 people eligible for town council, which has three elected members. Quantity A The number of possible combinations of council members, presuming no differentiation among office-holders. Quantity B The number of possible combinations of council members, given that the council has a president, vice president, and treasurer.

Possible Answers: Quantity B is greater. The relationship cannot be determined from the information given. Correct answer: Quantity B is greater. Explanation : This is a matter of permutations and combinations. Explanation : Begin by considering the three "hard and fast conditions" - the digits and the one upper-case letter.

In how many different orders can 8 players sit on the basketball bench? Possible Answers: 3, Correct answer: 40, Explanation : Using the Fundamental Counting Principle, there would be 8 choices for the first player, 7 choices for the second player, 6 for the third, 5 for the fourth, and so on.

Possible Answers: None of the other answers. Correct answer: 44, Therefore a bread recipe is a permutation. Calculating combinations and permutations We have to deal with 4 different cases: Permutations without repetitions Permutations with repetitions Combinations without repetitions Combinations with repetitions Permutations - selections when order matters 1. Permutations without repetitions How many ways are there to order 5 balls? Since this is a bit long to write out, we can write it out as 5!

Using factorial just means that we multiply all the numbers from 1 to our number, which is 5 in this case. What if we only wanted to choose three out of the five balls?

How many ways do we have to do that? Well we could just think about it as 5 choices in the first selection, 4 in the second, 3 in the third and that's it. It turns out that this strategy works for more items too. Permutations with repetitions How many ways are there to choose 4 balls out of our 5 balls from before if we can repeat ourselves?

Explanation : The fundamental counting principle says that if you want to determine the number of ways that two independent events can happen, multiply the number of ways each event can happen together. Report an Error. Possible Answers: Correct answer: Explanation : This is a permutation problem, because we are looking for the number of groups of winners.

Explanation : Since this a combination problem and we want to know how many different ways the cookies can be created we can solve this using the Fundamental counting principle. Possible Answers: million. Correct answer: 18 million. Explanation : The total number of possible combinations of a series of items is the product of the total possibility for each of the items. Explanation : The first person holds 7 hands.

Explanation : There are 5x4x3 ways to arrange 5 flavors in 3 ways. Explanation : You have 3 possible types of bread, 2 possible types of meat, and 2 possible types of cheese. Copyright Notice. Alonso Certified Tutor. Stan Certified Tutor. Northwestern University, Bachelor in Arts, Economics. Northwestern University, Unknown, Pre-Med.

Daniel Certified Tutor. Report an issue with this question If you've found an issue with this question, please let us know. Do not fill in this field. Louis, MO Or fill out the form below:. Think of it like a garden of forking paths where at the first fork you have to decide whether or not to include 1, then 2, then With each choice the number of possibilities doubles. Each combination refers to each set. If the empty set doesn't count as a combination, then it's If you can choose to use less of the items in a sequence that changes things.

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Learn more. How many combinations of 6 items are possible?