Given the word 'NOFIBRE':                                                                               In how many different ways can the letters be arranged? In how many different ways can the letters be arranged if the word start with a vowel letter? In how many different ways can the letters be arranged if the vowels always come at the end?

Q: Ten pirates find a sack of gold coins. When they try to divide up the gold (with equal shares for…

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Q: In how many ways can the letters of the word HORRAR be arranged if vowels are together?

A: Given information- We have given the letters of the word- HORRAR We have to find a number of ways to…

Q: A class has 28 students. In how many different way can four student form a group for an…

A: GivenTotal no.of students in a class(n)=28No.of students form a group for an activity(k)=4

Q: Suppose we want to choose 5 letters, without replacement, from 15 distinct letters. (a) How many…

A: Solution-: Here, n=15,r=5 We want to choose 5 letter, without replacement from 15 distinct letter.…

Q: Suppose we want to choose 5 letters, without replacement, from 14  distinct letters. (a) If the…

A: To find : If the order of the choices matters, how many ways can this be done?

Q: An employment agency has 8 temporary workers. (a) In how many ways could 5 of them be assigned to…

A: The agency has 8 workers.  (a) Out of the 8 employees can be selected in 8C5 = 56 different ways.…

Q: In how many ways can we arrange 3 boys and 3 girls in a circular table if:  All boys and girls are…

A: Given, 3 boys and 3 girls       To find, In how many ways can we arrange them if all boys and girls…

Q: How many different 4-letter radio-station call letters can be made   if the first letter cannot be…

A: Given: 4- letter radio-station call letter has to be made with first letter should not be A, B or C…

Q: There are 55 runners in a race. How many ways can the runners finish first, second, and third? There…

A: given data number of runners = 55 we have to find no. of ways to finish first ,second and third…

Q: 10 samples of different cakes are on display as customers leave a store, theyare told that they can…

A: When r number of objects are selected from total n number of distinct objects then the total number…

Q: In how many different ways can you arrange the letters of the word NONSENSE if the first letter and…

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Q: In how many different ways can a 4-child family have 2 boys and 2 girls?

A: To determine: Ways can a 4-child family have 2 boys and 2 girls.

Q: Six people are about to enter a cave in a single row. In how many ways could the arrange themselves…

A: Given: Six people are about to enter a cave in a single row

Q: In how many ways can seven people be seated at a round table if 2 particular people must not sit…

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Q: Twelve basketball players are to be seated in a round table.  In how many ways can the players be…

A: We know  n persons can be arranged in a circular table in (n-1)! ways.   Given, 12 basketball…

Q: n how many ways can 5 men, 4 women, and 3 children be arranged in a row of 12 seats if a. the men…

A: Given that  Number of men = 5 Number of women = 4 Number of children = 3 Number of seats in the row…

Q: Suppose we want to choose 5 letters, without replacement, from 17 distinct letters. (a) How many…

A: Solution:In this problem we want to choose  letters, without replacement, from  distinct letters.(a)…

Q: If there are 9 people and only 4 chairs are available , which of the following is the correct…

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Q: In how many different ways can four pennies, three nickels, two dimes and three quarters be arranged…

A: Pennies =4  Nickels = 3 dimes= 2 quarters = 3 The objects are 4 pennies, 3 nickels, 2 dimes and 3…

Q: In how many ways can 5 persons be seated in a room where there are 10 seats?

A: We have to find number of ways to seat people in room.

Q: In how many different ways can eight people be seated in a row?

A: Different ways that eight people can sit in a row.

Q: There are 42 runners in a race. How many ways can the runners finish first, second, and third? There…

A: there are 42 runners in a rece we have to find out the no. of ways can finish first, second and…

Q: There are 58 runners in a race. How many ways can the runners finish first, second, and third? There…

A: From the given information, total number of runners = 58. The objective is to find the number of…

Q: How many different ways can 5 out of 8 different shirts, 4 out of 10 different pairs of pants, and 3…

A: We have given that,  Shirts = 8 , pairs of pants  = 10 and pairs of socks = 6

Q: How many different ways can the letters of "jogging" be arranged? The number of different ways that…

A: The word “jogging” contains a total of 7 letters in which “g” letter is repeated 3 times.

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: In how many ways can  8 people sit around a round table if two particular people must sit next to…

A: Given  Number  of people =8  We want to find how many ways to 8 people sit around round table if two…

Q: In how many ways can 15 different pizza toppings be chosen from 22 available toppings? There are…

A: No. of available toppings=22No. of pizza toppings to be chosen=15

Q: Consider the 7 letters A, B, D, E, F, G and O. How many 3-letter words can be formed from the 7…

A: Hi, thanks for posting the question. Since there is more than one question posted. We will answer…

Q: How many ways can all the etters in the word EDUCATION can be arranged if all the vowels are right…

A: The word education has 9 letters in which 'AEIOU69f4fc43-162e-4e8b-82a6-efea9c821b47' are vowels.…

Q: How many different 10-letter words (real or imaginary) can be formed from the following letters? G,…

A: There are 10 letters; G, P, W, R, K, V, P, A, F, P

Q: In how many ways can 6 bicycles be parked in a row?

A:

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.