How many ways can 120 identical packages be loaded into 10 delivery trucks where some trucks may have no packages?

Q: Suppose Pat has eight shirts and four pairs of pants. How many different outfits  can Pat make by…

A: The person has 8 shirts and 4 pairs of pants and he can make one outfit by combining one shirt with…

Q: A restaurant offers 20 appetizers and 40 main courses. In how many ways can a person order a…

A: Multiplication rule of counting:If a task consists of a sequence of choices in which there are ‘a’…

Q: How many ways can first and second place be awarded to 12 racers?

A:

Q: How many different ways can a theatrical group select 2 musicals and 3 dramas from 11 musicals and 8…

A: Given,no.of musicals=11no.of dramas=8

Q: how many way can six books be arranged on a shelf

A: We need to find the number of ways for arrangement of six books on a shelf.

Q: a family wants to adopt 2 cats and 3 dogs from a shelter that has 12 cats and 15 dogs. in how many…

A: The number of ways of selecting 2 cats from 12 cats is,

Q: How many ways can 12 students standing in a line be arranged if John must be first in line?

A:

Q: A typist has 5 letters and 5 addressed envelopes. In how many different ways can the letters be…

A:

Q: How many ways can 6 ladies be seated in a circular table such that 2 of the ladies must always sit…

A: To find: The number of ways to arrange 6 ladies in a circular table such that 2 of the ladies must…

Q: A business has hired 12 new employees and must assign 8 to the day shift and 4 to the night shift.…

A: We have given that  A business has hired 12 new employees and must assign 8 to the day shift and 4…

Q: In how many ways can 9 individuals be seated in a row of 9 chairs if two individuals wanted to be…

A: Permutation is the method that used to measure the number of arrangement in the data set. In this…

Q: How many ways can a cricket team of 4 bowlers and 7 batsmen be formed from a group of 8 bowlers and…

A: GIVEN DATA : There are 8 bowlers and 11 batsmen       TO FIND : Number of ways a cricket team formed…

Q: In how many ways can six books be lined up along a shelf?

A:

Q: A class of 20 students is divided into 5 teams of 4 students each. How many ways are there to divide…

A: Number of ways in which n students can be divided into k groups of h students is given by,

Q: . How many ways can 3 oranges be chosen from a fruit bowl that contains 11 oranges?

A: We are asked to find the number of ways to choose 3 oranges from 11 oranges

Q: There are 12 different books on a shelf. In how many ways can we take 4 of these books and put them…

A: Combination: A combination is a grouping or subset of items. for a combination, the order not…

Q: How many ways can 120 unique packages be loaded into 10 delivery trucks where each truck must have…

A: 120 distinct packages have to be distributed equally among the 10 trucks.

Q: In how many ways can you place 9 different books on a shelf if there is space enough for only 5…

A: Given, 9 different books on a shelf and there is space only for 5 books.

Q: how many ways can you arrange 23 books on a shelf that can only hold 7 books?

A:

Q: In how many ways can 7 people be seated on a sofa if it can only accommodate 5 people?

A:

Q: How many 4-letter words can be made from the letters MATH if repetition of letters is allowed?…

A: Given: Letters M , A , T ,H  We need to find number of 4 letter words that can be made.

Q: How many Licence plates of two letters followed by three digits can be made if the letters and…

A: Total no. of letter from A-Z is =26Total no. of digits from 0-9=10

Q: If I have 9 flower pots and 11 different flowers how many different ways can flowers be in each pot?

A: 11C9 ways. that is in 55 way.

Q: In how many ways can you arranged 2 Math books, 3 Science books and 3 English books if only one book…

A: The total number of mathematics books are 2. The total number of science books are 3. The total…

Q: How many ways can 8 CDs be arranged on a shelf?

A: To be found : Number of ways 8 CDs can be arranged on a self.

Q: How many ways can 11 DVDs be arranged on a shelf?

A: Given Number of ways can 11 DVDs be arranged on a shelf.

Q: How many Ways can 5 Pants, 5 Shirts and 2 Belt combination can be worn?

A: How many Ways can 5 Pants, 5 Shirts and 2 Belt combination can be worn?

Q: How many ways 4 people out of 20 can be sited on a bench for 4 persons?

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: A cleaning company has to clean 11 different rooms on a floor of a building. How many different ways…

A: Given: 11 different rooms

Q: How many ways can 8 DVDs be arranged on a shelf?

A: We can arrange 8 DVD's in 8! ways.

Q: How many different numbers of five digits can be made using the digits 2,2,3,3,3?

A: The objective is to find how many different numbers of five digits can be made using the digits…

Q: You are ordering an extra large pizza with multiple toppings on it. In how many ways can 8 different…

A:

Q: How many ways can five boys and five girls be seated alternately at a circular table?

A: Given: 5 boys and 5 girls are to be arranged in circular way alternately. The diagram can be…

Q: How many license plate containing two letter followed by three digit can be formed 2 If the letters…

A: License plate made up of 5 alphanumeric in which first two position taken by letters then last three…

Q: How many different license plates are possible if 2 uppercase letters are followed by 4 digits and…

A: A number plate consist of 2 uppercase letters followed by 4 digits, in which first digit cannot be…

Q: How many ways can 10 candles be arranged on a shelf?

A:

Q: How many ways can captain, co captain and team manager be assigned to a group of 10 runners at a…

A:

Q: How many license plates are possible if they consist of 1 digit followed by 1 letter followed by 5…

A:

Q: How many 3-letter words can be made from the letters MATH if repetition of letters is allowed?…

A: We have given that a four letter word MATH from which we can made 3 letter words in two different…

Q: how many different license plates are possible if each contains four english letters followed by…

A: Here total English letter 26  And digits are 0,1,2,....9 that is total 10 digits

Q: How many ways can my daughter put 50 pairs of shoes on 4 dolls?

A: Combination :  The number of ways to choose a sample of k elements from a set of n distinct objects…

Q: A pizza shop offers mushrooms, pepperoni, and onion for their pizza topping and 1 type of cheese.…

A: The number of ways of selecting r objects from n objects can be given by evaluating the expression .…

Q: In how many ways can 12 books be divided among 4 students so that each student receive three books?

A: Given that : Total books (n) = 12 Divided among 4 student and each student get books = 12/ 4  = 3 So…

Q: Before leaving for the day, the delivery trucks are loaded with packages. How many ways can 120…

A: There are n unique/distinct packages that must be loaded into 10 trucks in such a way that there are…

Q: 2. In a certain country, license plate numbers have 3 letters followed by 3 digits. How many…

A: here use counting principle  for combination  nr = n!(n- r)! r!

Q: How many ways can 3 men and 4 women be seated on a bench if the women to be together?

A:

Q: How many different ways can a visiting nurse visit 10 patients if she wants to visit them all in one…

A: A visiting nurse can visit 10 patients in 10! ways in one day.

Q: How many ways are there to seat 6 different boys and 6 different girls along one side of a long…

A: Given that, there are 12 persons and 12 seats. 12 persons includes 6 boys and 6 girls. Therefore,…

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.