The number of 3-permutations of 5 objects with repetition allowed is 51 / (5-3)! 35 5x3 53

Q: An instructor gets 5 calls in 3 hours 1.How likely is that the teacher will get exactly 10 calls in…

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Q: A contest consists of finding code words that can be formed from the letters “MEEST”. Assume that…

A: Given word MEEST, Letters = {M,E,E,S,T} Since the letter E is repeated twice then number of words…

Q: Suppose you had 4 red checker pieces and 5 black checker pieces. How many ways can you arrange these…

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Q: Find the number of ways of placing 12 balls in a row given that 5 are red, 3 are green and 4 are…

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Q: 4, and 6 if no digit is repeated in any number? a. b. repetitions are allowed?

A: We have to find the number of two digit numbers.

Q: Find the number of the permutation of 8 different things taken 3 at a time

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Q: A committee of 5 students is to be chosen from 6 boys and 5 girls 1. How many different 5-member…

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Q: How would I go about answering this question?

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Q: A garden has two rectangular flower beds.  In the first bed, we will plant five different flowers in…

A: Given that, A garden has two rectangular flower beds.  In the first bed, we will plant five…

Q: In each problem, please indicate what kind of permutations is involved, then solve. Show ypur…

A: Given that  1.. Seven runners join a race. In how many possible ways can they be arranged as first,…

Q: A box contain 8 red and 6 green balls. In how many ways can 3 balls be drawn such that 2 is red and…

A: GivenA box containNo.of red balls = 8No.of green balls = 6Total no.of balls = 14

Q: nd presently has 3 lots to build on

A: Given : a contractor builds homes of 6 different models and presently has 3 lots to build on.  we…

Q: A boy imagined four-digit multiple of 5 with different digits. If the first digit is erased, the…

A: Suppose the number be xyzw and x,y,z,w are different numbers. Now the number is multiple of 5. so W…

Q: Suppose that 4 Pistons need to be installed in a new engine block. there is a production run of 100…

A: Given, there is a production run of 100 Pistonsand 4 Pistons need to be installed in a new engine…

Q: How many words of  at most 4 letters can be formed with the letters of the word TUNE if letters…

A: We  have to find no of words .

Q: How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6 and 7 such that the…

A: To form a 3 digit number, we start we can not place 0 on hundreds position since that will make it a…

Q: Find the number of permutations using four different numbers (2,5,11,30) if they are taken 2 at a…

A: Given that, Four different numbers are (2,5,11,30) To find: Number of permutations using four…

Q: A 6-digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the…

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Q: How many ways are there to put 5 balls in 2 boxes if the balls are distinguishable and the boxes are…

A: Total number of distinct boxes=n=2 Total number of distinct balls=r=5

Q: suppose repetitions are not allowed. Find the number n of three-digit even nimbers that can be…

A: Given problem Given that   Suppose repetitions are not allowed. Given six digits : 2,3,5,6,7,9…

Q: How many 4-permutations of the multiset {A®, B®,C5,D²} exist?

A: claim- how many 4-permutation of the multiset A∞ , B∞ , C5 , D2exist ? as we know  number of r…

Q: Suppose any possible arrangement of 8 letters is considered a word and the letters are chosen from…

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Q: Suppose that you have a combination lock that uses letters instead of numbers for its combination,…

A: Solution: The total number of letters is 26 and the lock will be opened with four letters and…

Q: Suppose a designer has a palette of 12 colors to work with, and wants to design a flag with 5…

A: Given that a designer has a palette of 12 colors to work with, and wants to design a flag with 5…

Q: How many 4-permutations are there of a set of six objects?

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Q: Suppose 7 female and 6 male applicants have been successfully screened for 5 positions. In how many…

A: Given ,no.of females =7no.of males =6Total no.of peoples=13

Q: A committee has 10 members and 4 members must be chosen for a subcommittee. Three of the 10 members…

A: Statisticians/mathematicians use different counting techniques while selecting or arranging members…

Q: Find the number of permutations using 4 different letters a, b, c, and d, if they are taken 2 at a…

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Q: Suppose a n × n chessboard is missing two opposite corners. Prove that no matter what n is, you will…

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Q: How many subsets of set S = {1, 2, 3, 4, 6} do not contain odd numbers? Use bijection to solve this…

A: Solution S={1,2,3,4,6}

Q: How many three digit numbers can be formed from the digits 0,1,2,3,4,5,6,7,8 and 9 such that the…

A: Given numbers are, 0,1,2,3,4,5,6,7,8 and 9 Total numbers are 10 We have to calculate the number of…

Q: Spider has one sock and one shoe for each of its 8 legs. In how many different ways can the spider…

A: There are 8 socks and 8 shoes.

Q: How many strings of three decimal digits

A: Strings of three decimal digits:

Q: How many 8-digit telephone numbers are possible if the first digit cannot be zero and no repetitions…

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Q: A committee of 5 consisting of 3 girls and 2 boys is to be chosen from a class with 15 girls and 10…

A: Given: Total Number of Girls=15Total Number of Boys=10Commitee required 5 candidate in whichNumber…

Q: How many three-letter "words" can be made from 6 letters "FGHIJK" if repetition of letters (a) is…

A: Given 6 letters is "FGHIJK"

Q: How many four digit codes can be made out of the digits 0,2,4and 8 if the repetition of digits is…

A: We have to find four digit codes can be made out of the digits 0,2,4and 8 ....

Q: Suppose you are asked to arrange 10 books in a shelf. Three of them are Mathematics, 4 are English…

A: Let us assume there are three women A, B and C sitting beside each other. The different ways in…

Q: How many 4-digit numbers greater than 5000 can be formed from the digits 2, 4, 5, 7, 8, and 0?…

A: How many 4-digit numbers greater than 5000 can be formed from the digits 2, 4, 5, 7, 8, and 0?…

Q: A contractor builds homes of 9 different models and presently has 3 lots to build on. In how many…

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

Q: in 2  rows  there are  5 armchairs  and all are  occupied , in how many  differnt  ways can theses…

A: Given: Number of Rows =2. Number of armchair = 5. To determine the number of ways substitute the…

Q: How many ways are there to permute the elements of the multiset {1,1,2,2,3,4,5,6} so the first and…

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Q: A contractor builds homes of  11 different models and presently has 6 lots to build on. In how many…

A: We have to find the different ways can he arrange homes on these 6 lots...

Q: How many different license plates are possible if each plate consists of 2 letters followed by a 4…

A: here given license plates consist 2 letters followed by 4 digits

Q: If you have 12 boxes then how many balls do you have to put randomly into the boxes in order to…

A: Given that, We are having 12 boxes. In order to have atleast 4 balls in each box when a random box…

Q: . Find the number of permutations of the letters of the word ‘REMAINS’ such that the vowels always…

A: We can solve these questions using given details

Q: we have a 70% chance of winning a game and play 80 times, how many games do we expect to win? Again,…

A: we have a 70% chance of winning a game and play 80 times, how many games do we expect to win? Again,…

Q: Suppose 10 baseball players are available to be drafted by 4 teams where each team might win any…

A: Assume the number of players drafted in 4 teams are x , y , z and w. Total number of players = 10…

Q: Red and blue ceramic tiles are laid according to a pattern such that for every 22 red tiles used, 3…

A: Given that there are total 300 ties of Red and blue colour .according to pattern every 22 red…

Q: In how many ways can you take 3 letters from the alphabet (lower-case only) such that any character…

A: Here AS PER POLICY I HAVE CALCULATED FIRST MAIN QUESTION PLZ REPOST FOR REMAINING PARTS

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.