A committee has 1919 members. A subcommittee of 55 members must be chosen for a subcommittee. In how many ways can the 55 members be chosen for a subcommittee from the 1919 members?    Levi has 1414 books on his summer reading list. He wants to choose 66 books to read over the summer. In how many ways can he choose the books?

Q: if there are no restrictions? if Holly and Sam cannot sit together?

A: here given ,  Holly, Parker, Jace, Ola, Amir and Sam have gone out to a football game together, They…

Q: Sandra is writing an article and taking pictures for the school newspaper. She chooses three…

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Q: Twelve people are on a committee. If five of them are to be chosen to serve on a subcommittee, how…

A: There are total 12 people.  Since it is a group of people so order does not matter. So we will use…

Q: Don has two pairs of shoes, six pairs of pants, and six shirts. If all items are compatible, how…

A: Given that Don has two pairs of shoes, six pairs of pants, and six shirts. If all items are…

Q: Paula’s Pie Shop offers 23 different pie fillings, each available in 8 different sizes and 4…

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Q: A value meal package at Ron's subs consist of a drink, a sandwich, and a bag of chips. There are…

A: Types of drinks=5Types of sandwich=4Types of chips=2

Q: You have 6 different video games. How many different ways can you arrange the games side by side on…

A: Given,Total no.of video games=6

Q: Mr. H has a collection of 500 vessels. In how many ways can he name his favorite and second favorite…

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Q: Jonathan likes to randomly mix-and-match the colors of the shirts and pants he wears to school. His…

A: The objective of this question is to find the total number of possible combinations of shirt and…

Q: Please answer step by step. Thank you! Decide the number of possibilities of the given situation:…

A: It is required to pick 3 questions from a bank of 39 questions. n=39 r=3

Q: The Wycoffs are planning their next family night. They always have dinner out somewhere and then do…

A: The answer is attached below,

Q: Select a committee of seven members from a group of six women and eight men. The order of selection…

A: Given that  A committee of seven members  Group of 6 women and 8 men

Q: There are 15 people eligible to receive 4 different awards.  The awards are in the amounts of $50,…

A: Given: There are 15 people eligible to receive 4 different awards. The awards are in the amounts of…

Q: A toll collector on a highway receives $8 for trucks and $7 for cars. At the end of a 3-hour period,…

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Q: Decide whether you would use a permutation, a combination, or neither. Next, write the solution…

A: The objective of this question is to determine the number of ways a committee of five persons can be…

Q: Four math clubs go to a conference and meet up for lunch. They introduce themselves to each other…

A: The scenario in which four math clubs go to a conference and meet up for lunch.Every member of each…

Q: There are 9 different types of dressing at a store. How many different orders can the stocke place 5…

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Q: Agustina owns all five books in the Spiderwick Chronicles series. In how many different orders can…

A: Given: Number of books = 5

Q: Suppose you want to get a license plate. The license plate has to have 3 letters without repetition,…

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Q: The Moore family received 31 pieces of mail on April 27. The mail consisted of letters, bills,…

A: Moore family recieved 31 pieces of mail mail consists of letters (L), bills (B) , Magazines (M) and…

Q: Tell wether each problem represets a permutation or a combination. Then solve the problem. Brandon…

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.