Consider a regular deck of cards with 52 cards. In how many ways can we shuffle the deck if all the red cards must be on top of all the black cards?

Q: 2. In a group of 45 students, 23 take history, 18 take biology and 10 take both history and biology.…

A: Given :  Total number of students = 45 Number of students taking history = 23 Number of students…

Q: Q2) A club has 20 member a) In how many different ways could the club choose a president and a vice…

A: Combination only includes number of ways of selection whereas, permutation includes number of ways…

Q: Adam, Bill and Carl had some trading cards. Bill had 1 as many cards as Adam. 3 of his cards and…

A:

Q: 1. Larry had 1/3 as many balls as Andy. Andy gave 8 balls to Larry so that they would each have the…

A:

Q: In a music club with 16 members, 5 people played the piano, 11 played the guitar, and 3 didn’t play…

A: let A= set of  people in the club who played pianoB= set of people in the club who played…

Q: A teacher wants to assign 4 different tasks to her 4 students. In how many possible ways can she do…

A: Solution

Q: girl has 9 skirts, 10 blouses, and 4 pairs of shoes. How many different skirt-blouse-shoe outfits…

A: Given that the girl has 9 skirts, 10 blouses and 4 pairs of shoes.

Q: Let a, b, c be three consecutive odd nubmers, with a < b < c. What is the  value of a2−2b2+c2?

A:

Q: A bag contains 6 red balls and 4 white balls. In how many ways can one draw: a) 2 white balls b) 2…

A: As per our guidelines, we are allowed to answer first three sub-parts only. Thanks   6 red balls  4…

Q: A teacher is decorating their classroom by placing posters in a row on one wall. The teacher has 7…

A: Explanation: a) Given that,  Choose 5 posters out of 7. P57=7!(7-5)!=7×6×5×4×3=2520

Q: 1. Haniemay wants to try all the 23 dishes and 6 desserts in offered in PUP lagoon but she is…

A:

Q: In a class of 40 students, 26 like Math, 12 like physics, and 6 like both math and physics.…

A: Solution: From the given information, number of students in a class is 40. Number of students like…

Q: A baseball team takes a road trip and plays 6 games. In how many ways can they win 4 and lose 2…

A:

Q: A person buys 32 one-liter bottles of soda bottles for a large company party. The store clerk offers…

A: given : total number of bottles = 32  bottles held by 1 cardboard case = 8 to find : number of…

Q: Answer the problem involving permutations and combinations. SHOW YOUR SOLUTION. 1.) In how many…

A: (1) No.of senators selected in a committee,r = 6 Total no.of senators,n = 12 The  no.of ways can…

Q: 1. Yana wants to travel and visit caves in the Philippines. However, because of tight budget, she…

A: Note : As per Bartleby's guideline for more than one questions only first is to be answered please…

Q: A Convener and a Secretary are to be chosen from group of people consisting of 50 people. Explain…

A: i) We can select A as Convener in only 1 way. We can select Secretary from (50-1)=49 people in 49…

Q: In a group of 15 students, 6 students are girls.  In how many ways can a team of 10  students be…

A:

Q: Christine wants to invite three of her friends from four married couples to play tennis with her.…

A: There are 4 married couple. That is total there are 8 members. Out of 8 members, Christine wants to…

Q: Four married couples have bought 8 seats in the same row for a concert. In how many ways can they be…

A: Given problem Given that   Four married couples have bought 8 seats in the same row for a concert.…

Q: For this problem, assume that 13 exhibits entered the science fair and that we want to assign 4…

A: From the provided information, Total exhibits = 13 Total prizes = 4

Q: How many ways are there to go from B to D?

A: here given  A boy lives at B and wants to go to school at D. From his home B he has to first reach C…

Q: In the 4th volume of the shintim, Krim, Po, Jen, Quill, and Dart are bound to travel on Trempo. They…

A: Let us assume the following events Ri - Rock is shown by the individual i. Pi - Paper is shown by…

Q: ianist plans to play 6 pieces at a recital from her repertoire of 26 pieces.  How many different…

A: Total number of pieces available (n) = 26 pieces. Number of pieces (r) which a pianist needs to play…

Q: How many blocks are needed to build an​ up-down-up staircase with 5 steps up and 5 steps​ down?

A: To solve the given problem

Q: Of 100 employees of a store located in downtown Boston, 36 people take the subway to work, 24 take…

A:

Q: A row of six seats in a classroom is to be filled by selecting individuals from a group of ten…

A: Use the fundamental principle of multiplication. As per the fundamental principle of multiplication,…

Q: A box of Mrs. Donuts contains 8 honey dipped, 6 bavarians, and 7 chocolate filled donuts. How many…

A: Given,no.of donuts honey dipped=8no.of bavarians donuts=6no.of chocolate donuts=7

Q: Four married couples have bought 8 seats in the same row for a concert. In how many different ways…

A: = Given that ,4 married couples have bought 8 seats in same raw for concert .which means there are 4…

Q: In a math 105 class of 32 students, a survey showed that 20 students used the ALEKS etext at least…

A: Given,no.of students used ALEKS etext at least once=20no.of students used video at least…

Q: Is 40% of 30 equal to 30% of 40

A: Let 'x' represents the quantity 40% of 30, and 'y' represents the quantity 30% of 40. Simplify 'x'…

Q: 4. If Lucy picks 12 bushels of apples, which option should she choose? 5. How many bushels of apples…

A:

Q: 5 If you have a party for 70 people and your require 8 Ibs. of baby spinach for salads to feed them…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: A teacher decided to buy breakfast for her students while welcoming them during the first day of…

A: Inclusion exclusion principle Let A, B be two events then the number of ways to get either A or B'…

Q: Q2: a group of 6 boys and 4 girls, in how many way four children can be selected such that at least…

A: Given is a group of 6 boys and 4 girls.   To Find: Number of ways four children can be selected such…

Q: 4.) How many cards should you pick in a deck making sure that at least two of the cards will be…

A: Solution: 4) 41 There are 13 spades . So to ensure at least 2 spades are there are 41. Suppose 39…

Q: Decide whether the exercise involves permutations or​ combinations, and then solve the problem.   In…

A: (a) Given: It is given that, A club has 11 male and 10 female members.  To find: How many committees…

Q: Assume that the camper has 5 jackets, 3 sleeping bags, and 14 different packages of food. An outfit…

A: Combination is the way of selecting a units from a set without considering position of order. The…

Q: A builder is planning to build 12 houses along one side of a road. He will build 2 houses in style…

A: Given data: The total numbers of houses are n=12. The number of styles A house is A=2. The number of…

Q: ملاحظة: اجب عن ثلاثة افرع Q2) A club has 20 member a) In how many different ways could the club…

A: Introduction: The permutation is the act of putting all the members of a set into a sequence or…

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

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

Q: In how many ways can 3 men and 3 women sit in a row of 6 chairs, if... a) There are no restrictions?…

A: HERE GIVEN  NO OF MEN =3 NO OF WOMEN= 3

Q: You are to form 3-digit numbers from the digits 1 to 5. How many 3 digit numbers can be formed if a)…

A: Solution of given question is written in below steps.

Q: Mr Regpala needs the help of 6 students from the class to help him move some supplies. If the class…

A: Given that  Mr Regpala needs the help of 6 students from the class to help him move some supplies…

Q: Q2) A club has 20 member a) In how many different ways could the club choose a president and a vice…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Twelve classmates are taking a picture side by side.  A. In how many ways can they take the picture…

A: Given , Twelve classmates are taking a picture side by side.     (a) In general, n distinct objects…

Q: A student is to answer 10 out of 13 questions on an exam. (i) How many if he must answer exactly 3…

A: It is an important part of statistics . It is widely used .

Q: Solve by the method of your choice: In a race in which six automobiles are entered and there are no…

A: We have to find ways in which first four finishers come in.

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.