14. If there are 31 flavors of ice cream How many different ways can you choose 2 scoops if you can have 2 scoops of the same flavor?

Q: Suppose there are 21 different competitors at a barbeque competition. Judges are going to award 5…

A: Given: 21 different competitors The total award is given = 5

Q: In how many ways can 2 pizza toppings be chosen from 12 available toppings? Your answer is :

A: Consider the formula for the n objects taken r at a time is, Cn,r=n!r!n-r! Then, the number of ways…

Q: 4. Suppose Pat has eight shirts and four pairs of pants. How many different outfits can Pat make by…

A: Every shirt combines with every pair of pants to make an outfit.  Shirt 1 creates an unique outfit…

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: In how many ways can 2 pizza toppings be chosen from 12 available toppings?

A: We have given that 2 pizza toppings be chosen from 12 available.

Q: A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without​ looking, how many…

A: Given: There are total 4 oranges, thus it is not possible to get 5 oranges.

Q: 38. How many different committees can be formed from 5 professors and 15 students if each committee…

A:

Q: How many ways can 3 teachers and 4 veterinarians be seated on a bench with the teachers seated…

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

Q: In how many ways can 4 pizza toppings be chosen from 12 available toppings? Your answer is:

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: In how many ways can 10 people be seated on a bench if only 4 seats are available?

A: Given problem Given that   In how many ways can 10 people be seated on a bench if only 4 seats are…

Q: How many license plates consisting of three letters followed by three digits contain no letter or…

A: Here we have to find  out the combination of licence plate where repetition  of  letters and digits…

Q: How many ways can five people A , B , C , D and E sit in a row at a movie theatre if D and E will…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: 1. Given 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

A: Note: According to Bartleby guidelines expert solve only one question and rest can be reposted.

Q: 4. If your bag has 60 Smarties, and 30% of the Smarties are purple, how many purple Smarties do you…

A: Since you have asked multiple questions in single request so we will be answering only first…

Q: 2. How many ways can a postman post 3 letters in 5 letter boxes?

A:

Q: 4. A chef can prepare 20 different dinners. In how many ways can he select 6 of them for today's…

A: 4. Answer: In 38760 ways can he select 6 of them for today's menu out of 20.

Q: If 3 Americans, 4 British people and 2 French people are to be seated in a row, how many seating…

A:

Q: In a bag containing 5 white balls and 6 black balls, how many ways can we draw a white or a black…

A:

Q: How many ways can a jury of 5 women and 6 men be selected from 13 women and 12 men

A:

Q: In how many different ways can 12 people occupy the 12 seats in a front row of a mini theater ?

A: Given: The number of seats available is 12.  The number of people to be arranged in seats is 12.

Q: How many ways can you select a committee of 4 student our of 10 students?

A: As per our guidelines we are suppose to answer only one question4)Given Total no.of…

Q: In how many ways can you choose 3 gifts from a bag containing 4 different gifts?

A: It ia given that Total gifts n  = 4 Selected gifts r = 3

Q: How many ways can Marie choose 22 pizza toppings from a menu of 66 toppings if each topping can only…

A: Note: Thank you for the question. The question is considered as choosing 2 pizza toppings from a…

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

A: Given data, Number of red balls=6 Number of white balls=4 In how many ways can one draw 2 balls of…

Q: a) in how many ways can 6 numbered books be distributed over 4 identical shelves if shelves can be…

A: To distribute n things in k places, the formula is n+k-1k-1

Q: 11. In how many ways can 4 boys and 5 girls sit in a row if the boys and girls must alternate?

A: Disclaimer: Since you have asked multiple questions, we will solve the first question (i.e. #11) for…

Q: 6. How many outfit combinations can be put together from 6 shirts, 3 pairs of pants, and 4 pairs of…

A: Total shirt = 6 Total pants = 3  Total shoes =4

Q: 1. Suppose Ivana has 4 shirts, 3 pairs of pants and 3 pairs of shoes. How many different outfits can…

A: Given: Ivana has 4 shirts, 3 pairs of pants and 3 pairs of shoes. The total different outfits Ivana…

Q: 2. In your drawer, there are 4 identical pairs of brown socks and 8 identical pairs of green socks.…

A:

Q: How many different ways can a group of 5 students line up to get ice cream?

A: This is type of permutation question, because here the order of placing the people in the place…

Q: In how many ways can 5 men and 5 women be seated at a round table if each woman is to be  between…

A: We have round table and 5 men and 5 women be seated at round table if each women is to be between…

Q: 19.In how many ways can 4 girls and 3 boys be arranged around a camp fire if the 4 girls must be…

A:

Q: How many ways can 12 people line up if Joey and Sally must be next to each other?

A: here given group of 12 people arrange in raw   and arrange around round table

Q: 2. Af East Middle School, 28% of the students are in the band. If 168 students are in the band, then…

A:

Q: 1. How many students like either Realistic Fiction, Mystery or both? 2. How many children like all 3…

A: Hi, Thank you for the Question. Since you have posted multiple questions we will answer the first…

Q: 3. If ice cream is served in a cone, in how many ways can Abby choose her three-flavored ice cream…

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: 2. In how many ways can 3 men and 4 women be seated on a bench if the women must be seated together?

A: Note: Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: How many outfit combinations can be put together from 8 shirts, 4 pairs of pants, and 2 pairs of…

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: (i) How many ways are there to seat five different boys and five different girls along one side of a…

A: There are 10 seats in total. There are 5 boys and 5 girls to be seated. There is no restriction on…

Q: In how many ways can 6 boys and 7 girls sit in a row if the girls and boys must alternate?

A:

Q: A school committee needs 2 more students. How many ways can the committee be selected from a group…

A: Given Data: The total number of students in the group is: n=10 The number of students required is:…

Q: How many ways can 3 baseball players and 2 basketball players be selected from 9 baseball players…

A:

Q: (i) How many ways are there to seat five different boys and five different girls along one side of a…

A: (i)

Q: _6. Rylan's basketball team has 11 players. How many ways can his coach choose five starting…

A: Given;  1): No of player =11  To choose 5  starting players from the 11 players then nonof ways ?…

Q: 6) The ski club with twelve members is to choose three officers captain, co-captain & secretary, how…

A: To find the number of ways

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: 13. How many license plates consisting of two letters followed by two number repetition is allowed?

A: To find: the number of number plates.

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.