n-factorial, n!, is the number of ordered arrangements of n distinct items repetition not allowed n! = n(n – 1) • • • • • 3 • 2 • 1. Start of Questions How many ways can 6 DVDs are arranged on a shelf?

Q: Consider the 6-digit numbers, with distinct digits (no repetition), that can be formed using the…

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Q: 2. How many different 6 letter strings can we make with only the letters J, E, R, M, Y, given the…

A: We have to use proper permutations and combinations.

Q: 7 identical prizes are distributed to a group of 21 people. How many ways are there to distribute…

A: The given details: 7 identical prizes are distributed to a group of 21 people. That is, Number of…

Q: How many words can be formed from the letters of the following words using all letters when no…

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

Q: Count the number of distinct ways of putting 3 balls into 4 boxes when: MB all boxes and balls are…

A: Permutation is a technique in which we determine the possible number of arrangements in a set in…

Q: In a bag there are 3 red balls, 2 blue balls, and 4 yellow balls. The experiment consist of drawing…

A: (a). Check whether the order of selection matters or not: The number of red balls is n(R) = 3. The…

Q: 0.) Attending plays: While visiting New York City, the Nygens want to attend 3 plays out of 10 plays…

A: Given total number of plays = 10 number of plays want to attend = 3

Q: troupe of 8 dancers is going to line up on stage. Of these dancers, 4 are wearing blue and 4 are…

A: Topic:- permutation and combinations

Q: a lot has 10% defective items. ten items are chosen randomly. the proability that exactly 2 of the…

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Q: standard deck of 52 cards and laid out in row on a table. In how many ways can this be done such…

A: Formula  Probability = Favorable Outcomes / Total Outcomes

Q: ich there are no repeated digits?

A: Available digits:   0,1,2,3,4,5,6,7,8,9 Total availeble position: 3 position   1st digit  2nd…

Q: A permutation is an ordered arrangement order matters  r distinct objects are chosen from n…

A: Number of  ways in which  first, second, and third prizes be awarded in a contest with 825…

Q: c) For a concert with 1000 fans, 6 lucky fans are chosen to perform duets with the singer (in a…

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Q: A bookstore manager wants to select one novel from each category. There are 3 different fantasy…

A: Given that , A bookstore manager wants to select one novel from each category. There are 3 different…

Q: Number of ways to give out 3 prizes to 20 people if all the prizes are the same. a. Combination b.…

A: We have to find given combination and permutattion.

Q: I need help on part B

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Q: Select the correct choice that completes the sentence below. The number of permutations of n…

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

Q: An organization sponsored a raffle where they were to sell all 500 tickets sequentially numbered…

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Q: Find the permutation. A picture is to be taken by lining up 5 of the 13 players of volleyball on…

A: Topic =  permutation

Q: Question: How many unique sequences of 3 symbols that can be formed from 9 symbols? Answer:…

A: Given that there are total number of 9 symbols. A unique sequence of three symbols have 2 or 3…

Q: We have an ordered sequence of 12 Good accounts and 5 Bad accounts as below. How many "flips" do we…

A: @solution::::   From the given information we have12 = Good records5= terrible…

Q: 25 Evaluate the sum: 4k²) - k=1

A: Explanation of the solution is given below..

Q: 4. How many four digits numbers can be formed with the 10 digits 0, 1, 2, 3......9 a. if repetitions…

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Q: Suppose a,b,n are integers and n>0 s.t. 63a^5b^4=3575n^3, what is the smallest possible n. Explain…

A: The objective is to find the smallest value of n such that 63a5b4=3575n3.

Q: PERMUTATION n! The number of different ways to arrange m objects out of n objects is given by „P…

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Q: Select the correct choice that completes the sentence below. The formula for the number of…

A: We want tell you which one is the correct choice.

Q: Bereken n. / Calculate n. 3(n + 1)! (n – 1)! 126

A: Given: 3n+1!n-1!=126n+1!n-1!=42n+1nn-1!n-1!=42nn+1=42

Q: 5. Forming a committee from members of a club does not show an important arrangement. How can you…

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Q: How many ways are there to pick 9 balls from large piles of (identical) red, white and blue balls,…

A: To determine the number of ways to pick 9 balls from large piles of red, white, and blue balls, plus…

Q: 7. During the New Year celebration there are orange, purple, blue, and green fireworks. In how many…

A: Given Fireworks Colors = Orange , Purple, Blue and Green

Q: Show combination notation in solving the problem below. A box contain 6 distinct red balls and 4…

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Q: How many ways are there of selecting an outfit that consists of one top (out of three tops) and one…

A: We need to select an outfit consisting of one top and one pair of jeans, While there are three tops…

Q: Fundamental Principle of Counting 1. A men's department store sells 3 different suit jackets, 6…

A: We have to find no. Of ways to arrange suits.

Q: 5. Suppose repetitions are not permitted. (a) Find the number of three-digit numbers that can be…

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Q: (b) Give two different interpretations of the bino- mial coefficient (") for non-negative integers n…

A: First we will give two different interpretations of the binomial coefficient nk for non-negative…

Q: Number of ways to give out 3 prizes to 40 people if all the prizes are different. a. Permutation…

A: Number of ways to give out 3 prizes to 40 people if all the prizes are different.   a. Permutation…

Q: How many permutations are there of the following word? COMBINATORICS permutations

A: Given word is COMBINATORICS'c' is repeated 2 times'o' is repeated 2 times'I' is repeated 2 timesand…

Q: Picking an integer between 0 and 9, inclusive, and repeat it for 35 times, how many prime numbers…

A: Consider the provided question, Picking an integer between 0 and 9, inclusive, and repeat it for 35…

Q: Using the rules for counting permutations and combinations of r things out ofn things. n! n! P(n,r)…

A: a) Find the number of ways can a president, vice-president and secretary be picked from the 19…

Q: . PERMUTATIONS How many 3-digit numbers can be formed from 3 one’s, 3 two’s, and 2 three’s?

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Q: ] 8. In a company telephone tree, each employee is to phone two other employees. In the first round,…

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Q: mbinations and Permutations How many ways can choose 20 friends to be invited to the party out of 25…

A: As we know that the choice of r element out of n elements is:- nCr=n!r!(n-r)!

Q: Four people are chosen from a group of seven people. Describe a situation of this case that involves…

A: Combination:   It  is a selection of objects where the order of selection is not important.   If n…

Q: committee of 5 students is to be selected from 14 students in a fraternity. In how many ways can…

A: Solution

Q: umber of ways you can wear 10 outfits to school each day in a 5 day week. a. Combination b.…

A: Given data, Number of outfits n=10 Number of days in a week r=5

Q: 8. A race involves 10 participants. In how many ways can 14, 2nd, 3rd and 4th place occur? In how…

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Q: 5. Mo has 140 songs on his mp3 player. a) How many different possibilities are there for the first…

A: Topic:- permutations and combinations

Q: 6. In a lottery game, 6 numbers are drawn from a machine with 40 balls numbered from 1 to 40. The…

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Q: UESTION 12 Suppose there were 500 nurses graduating this year. Assume that 400 were registered…

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Q: How many four-letter sequences are possible that use the letters q, u, a, k, e, s at most once each?

A: Use permutation and combination

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.