A woman has 11 close friends. In how many ways can she invite 5 of them to dinner if two of them are not on speaking terms and will not attend together?

Q: During a birthday party, how many ways can five guests, both parents, and the birthday celebrant be…

A: Follow the steps.

Q: In how many ways can 6 boys and 6 girls be seated around a circular table if all the no girls are…

A:

Q: In how many different ways can the director of a research laboratory choose two chemical engineers…

A:

Q: How many ways can 5 friends sit in a row at the movie theatre if Darren and Dave are in an argument…

A: If there is no restrictions then 5 friends can arrange in 5!=120 ways among themselves. If Dave and…

Q: A woman has 11 close friends. (i) In how many ways can she invite 6 of them to dinner? (ii)  In how…

A: Total number of friends are 11.i Number of ways in which she can invite 6 of them.C611=11!6! 5!…

Q: if a team of four players must be made from 8 boys and 6 girls, how many teams can be made if a.…

A:

Q: In a school with 92 students, 47 live with their biological father and 68 like with their biological…

A: Let S= total students  F= who lives with biological father M=who lives with biological mother Given…

Q: A club with five members is to choose three​ officers: ​ president, vice-president, and​…

A:

Q: Given a deck of 52 playing cards, in how many ways can a hand of 5 cards be dealt such that all are…

A: Given: The total number of cards in a deck is 52. The total number of the numbered cards in a deck…

Q: In a recent survey of 100 students, 38 said that they took a Math class as a freshman, 49 said that…

A: Follow 2nd step.

Q: A survey of 800 households revealed that 300 had only a TV, 200 had only a computer, and 100 had…

A: Given that, A survey of 800 household revealed that, 300 had only a computer and 100 had neither a…

Q: Out of 9 children, in how many ways can a family have at least 1 girl?

A: We have given that, 9 children i.e. n=9 and family have at least 1 girl i.e. r=1   Combination…

Q: An equestrian club has ten members. If the club wants to select a president, vice president, and…

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Q: A job interviewer has set 10 questions with four answer options and one correct answer. In how many…

A: The number of ways for two events to occur in a sequence is p×q. Here, p is the number of ways the…

Q: The mathematics department at WCC has 19 full-time faculty members; 10 female faculty members and 9…

A: Given that Full time faculty member=19 10 female faculty members and 9 male faculty member

Q: In how many ways may Ana select 5 of her 10 friends to attend her birthday party? In how many ways…

A: Here use combination

Q: Federal Express driver must make ten deliveries to ten different addresses. In how many ways can she…

A: factorial of n items gives you the number of ways you can arrange the given items

Q: A club of 136 members is in the process of choosing a president, a vice presider secretary, and a…

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Q: A committee of 6 people, with three of the six to be designated chair, vice-chair, and secretary, is…

A: 5. In a group there are 15 people. A committee of 6 people has to be selected, in which 3 must be…

Q: In a birthday party, 2/3 of the children were 8 years old, 2/3 of the remaining are 9 years old, and…

A:

Q: A club with eighteen members is to choose three officers: president, vice-president, and…

A: topic - permutations and combinations

Q: A classroom has 8 vacant chairs, 3 in the front row and 5 in the back row. In how many ways can 5…

A: Let us assume there are three students A, B and C sitting beside each other. The different ways in…

Q: In how many different ways can the director of a research laboratory choose two chemists from among…

A: Solution: Given information: Chemists applicants = 11  Physicists applicants = 7   To choose 2…

Q: In how many ways can you invite one or more of your five friends to a party?

A: There are total 5 friends available among which 1 or more than 1 friends can be invited to the…

Q: The mayor, together with 4 of his councilors is holding a meeting with 6 city volunteers. How many…

A: It is given that the mayor and 4 councilors is to attend the meeting with 6 city volunteers.

Q: 3. Anabelle would like to invite 9 friends to go on a trip but has room for only 5 of them. In how…

A: Question: Anabelle would like to invite 9 friends to go a trip but has room for only 5 of them . In…

Q: in how many ways can a hand of 5 cards be dealt such that 2 are black and 3 red cards?

A: Given:  There are 52 cards on the deck. There are 26 red and 26 black cards on the deck. Formula…

Q: In a class of 18 girls and 15 boys, in how many ways can a girl get the highest grade, a boy second,…

A: Consider the given information.The number of the boys is 15 and the number of the girls is 18 girls.

Q: Suppose the group of twelve consists of five men and seven women. a) How many five-person teams can…

A: A group consist of fire men and sexes women. We have to make a fire person team with 3men and 2…

Q: 2) Abby is adopting kittens from the pet store. If there are 18 kittens, how many ways can she…

A: In this question we have to find in how many Abby choose two kittens if there are two kitten .

Q: The soccer team has 20 members and will elect P, VP, T and S. In how many ways can this be done?

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Q: There are five people at a volleyball tournament. In how many ways can a team of three be chosen?

A: The number of ways r items can be chosen out of n items is equal to C(n,r) . The formula for C(n,r)…

Q: The newest cars have 12 different accessories and the buyer pays for each one separately.  If a…

A: Given, The newest cars have 12 different accessories A buyer wants to buy four accessories

Q: The number of ways of choosing ten students from a class of twenty-five is the same as the number of…

A: So in this we have to find the both then evaluate to see both are same so for this I'm providing…

Q: There are 15 persons in a party and if each 2 of them shakes hands with each other, how many ways…

A: Given data: 15 persons in a party Each 2 of them shakes hands with each other

Q: There are 50 guests in a party. If each guest shakes hands with all other guests, how many…

A:

Q: If there are 4 roads from Town A to Town B and 6 roads from Town B to Town C, in how many ways can…

A: Solution:  It is given that there are 4 roads from town A to town B and 6 roads from town B to town…

Q: From a club of 16​people, in how many ways can a group of six members be selected to attend a​…

A:

Q: n a class of 280 first year students, 65 study only Spanish, 100 study Chemistry, 175 study…

A: Given: There are 280 students in a first year class. 65 students study only Spanish. 100 students…

Q: In how many ways can the Principal and the 8 Headteachers of the different departments be seated in…

A:

Q: If a family has four children, in how many ways could the parents have two boys and two girls?

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Q: Suppose that you must choose three people to meet with a customer. You have nine people to choose…

A: Given data, Total number of people (n)=9 Number of people to meet with a customer (r)=3

Q: Mr. Ocampo buys chocolates in boxes of 48 and then puts them into groups of 11. If he buys 93 boxes,…

A: According to the question, we have to find the number of boxes left over after putting 93 boxes into…

Q: In how many ways can six medical technology students be seated in a round table if two of the six…

A: The number of ways n people can arrange in a seating order is (n!).

Q: In how many ways can Mrs. Smith give a chocolate bar, a bag of potato chips, and a can of cane juice…

A: Mrs. Smith give a chocolate bar , a bag of potato chips and can of cane juice to 3 of the 21…

Q: How many ways can 10 people line up if Joey and Sally cannot be next to each other? If the same…

A: here we have to use permutation ( arrangement )  Number of way r object can be arranged by taking…

Q: There are seven boys and five girls in the debate squad at Franklin High School. In how many ways…

A: Given: Number of boys = 7 Number of girls = 5 Number of members selected = 4 Number of boys required…

Q: If there are 9 apples and my sister ate 3, how many apples are left?

A:

Q: A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6…

A: