How many ways are there for three men and six women to stand in a line (a) so that all women stand together? (b) all men stand together?

Q: 4.) Last week Olivia power walked 2 miles per day on each of the 7 days. During the same week, she…

A:

Q: If n(A ∪ B) = 60, n(A ∩ B) = 40, and n(A) = n(B),find n(A).

A: Givenn(A∪B)=60n(A∩B)=40n(A)=n(B)To find n(A)

Q: If n(A ∪ B) = 50, n(A ∩ B) = 10, and n(B) = 20,find n(A).

A: Given,n(A∪B)=50,n(A∩B)=10 and n(B)=20 To find: n(A) Solution: We know,…

Q: If n(A ∪ B) = 96 and n(A) = n(B) = 67, find n(A ∩ B).

A:

Q: How many ways can 7 students standing in a line be arranged John must be first in line and Chloe be…

A: The number of ways in which n different objects can be arranged, is given by n!, where,…

Q: A restaurant wants to prepare meals for 4 customers. In the restaurant there are only 2 kinds of…

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Q: If  n(A) = 105, n(A ∪ B) = 144, and n(A ∩ B) = 46, find n(B).

A: We know from set theory nA∪B=nA+nB-nA∩B

Q: Answers must be in 4 decimals 1.At a breakfast buffet, 93 people chose coffee only and 47 people…

A: Solution According to guidelines we solve only first question

Q: animal shelter lines up 9 cages in a row. 4 of the cages contain cats and 5 of the cages contain…

A: Consider all the 4 cages of cats as 1 unit of cage. &, Consider all the 5 cages of dogs as 1…

Q: twenty tickets are entered into a raffle. 1st prize receives $100;2nd prize receives $25;3rd prize…

A: In theory of combinatorics, the way of selecting r objects from n objects with regard to the order…

Q: 'm thinking of three numbers . The product of two of them is 24, and the sum of all three is also…

A: There are three numbers.The product of two of them is 24, and the sum of all three is also 24. To…

Q: Consider two A.P.'s: S₁: 2, 7, 12, 17,... 500 terms and S₂: 1, 8, 15, 22, ... 300 terms Find the…

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Q: If n(A) =130, n(B) =135, and n(A ∪ B) =250, what is n(A ∩ B)?

A: According to the given information in this questionWe are going to find n(A and B)

Q: If  n(A) = 109, n(A ∪ B) = 160, and n(A ∩ B) = 42, find n(B).

A:

Q: Q:1 On a business retreat, your company of 20 executives go golfing.  (a) You need to divide up…

A: Given that: 20 executives go golfing. Group of 4 people the total number of ways possible can be…

Q: If n(A ∪ B) = 99 and n(A) = n(B) = 69, find n(A ∩ B).

A: Given, n(A ∪ B) = 99 and n(A) = n(B) = 69   The objective is to find  n(A ∩ B).

Q: 2. If the sum of three consecutive integers equals 60, what is the

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Q: If n(A) = 145, n(B) = 110, and n(A ∪ B) = 220, what is n(A ∩ B)?

A: Event:  The collection of outcomes in an experiment is called as an event. Addition rule:

Q: ways can they sit in a row if just the girls are to sit togetne. How many different signals, each…

A: Combination:The number of different selections of ‘r’ elements from a set of ‘n’ elements is denoted…

Q: 217 1 Karl had clips of four different colours. of the clips were white and 8 of the remaining clips…

A: Karl have 4 different colourd clips  1/8 of the total clips are white  2/7 of the remaining are red…

Q: 2) (-17) + (-22) + (-27) + (-32)..., A) -224 B) -448 C) -217 D) -218

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Q: 4.) Last week Rachel power walked 2 miles per day on each of the 7 days. During the same week, she…

A: A fraction is a number in the form xy (where x and y are both integers and y≠0). In the above number…

Q: The average of 3 numbers is between 7 and 10. The sum of the numbers could be any of the following…

A: Given that:-The average of 3 numbers is between 7 and 10.let, the three numbers are N1, N2 &…

Q: how many ways can a teacher sit 12 students in two rows of 6 chairs if Bobby must sit in the front…

A: Given: Total number of students = 12 Number of seats in each row = 6 Bobby is in first row and Billy…

Q: If n(A) = 104, n(A ∪ B) = 140, and n(A ∩ B) = 46, find n(B).

A: n(A) = 104 n(A ∪ B) = 140 n(A ∩ B) = 46

Q: You can choose from 25 flavours of ice cream and have enough money to get exactly 3 scoops. How many…

A: We need to find out the number of ways for the following.

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.