How many different ways can you arrange 2 letters from a set of 3 letters {L, S, U} such that repetition is NOT allowed but the arrangements are ordered? Show all those arrangements?

Q: Suppose we select 3 students randomly out of a class of 10 students to read a  paper from the…

A: Combination:   It is nothing but the objects are being selected when the order of selection is not…

Q: 2. How many ways can 10 books be arranged in a shelf if one of them is a bible and it must be placed…

A: Given that, 2.  10 books be arranged in a shelf & one of them is a bible and it must be placed…

Q: 1 red, 1 blue, 1 black, 1 yellow and 1 white car are all waiting at the traffic lights behind each…

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Q: In how many ways can 4 distinct red cars and 4 distinct black cars be parked in a row of 6 car…

A: Number of red cars = 4 Number of black cars = 4 Total number of cars = 8 Number of rows = 6

Q: How many 4-digit numbers can be formed from the digits 1,3,5,6, 8 and 9 if no repetition is allowed

A: Given : No. of digits (N) = 6 Digits : 1 , 3 , 5 , 6 , 8 , 9 4-digit no. can be formed i.e n = 4

Q: How many ways exist to arrange 7 books (A, B, C, D, E, F, and G on the shelf,  if the books B and

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Q: (a) How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible…

A: As we want our 3-digit number to be divisible by 5, the number 5 will be fixed on the unit's place…

Q: . Five-digit-numbers can be formed from the six digits 2, 3, 5, 6, 7 and 0. If repetitions are not…

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Q: Three cards are chosen without replacement from a deck of 52 cards and placed in order from first to…

A: In the deck of 52 cards, there are total 4 6's. (One for each of hearts, diamonds, spades and clubs)…

Q: a restaurant offers 2 different flavours of coffee 3 different soup selection. in how many ways can…

A: Two step multiplication principle: Assume that a taskcan be broken up into two consecutive steps.…

Q: A basketball team has 12 players on it. In how many different ways could a 5-player starting lineup…

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Q: Suppose we want to choose  3  colors, without replacement, from the  4  colors red, blue, green, and…

A: It is given that there 4 colors red,blue,green and purple.  and we need  to choose 3 colors without…

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: A staff car park at a university has 13 parking spaces in a row. There are 9 cars to be parked.…

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

Q: How many different ways can you arrange 2 letters from a set of 3 letters {T, S, U} such that…

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Q: In a college football training session, the defensive coordinator needs to have 10 players standing…

A: Given information Total players = 10 1 freshmen 2 sophomore 4 juniors 3 Seniors

Q: Suppose you are going to make a password that consists of 5 characters chosen from…

A: The given number of characters is n = 9, characters are: {2,3,6,7,a,c,k,n,p} In order to choose k…

Q: A license plate consists of   five symbols on each​ plate, where the first two symbols are letters…

A: Fundamental principle of counting : If an event occur in m ways an corresponding to it another event…

Q: How many combinations are there to pick r objects from 2n objects numbered from 1 to 2n with n > 2…

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Q: How many arrangement of 8 letters taken from 5 vowels and 21 consonants can be made if there has to…

A: 21 consonants and 5 vowels. Given condition, 8 letter words using 5 consonants and 3 vowel.…

Q: How many 5-digit numbers can be formed using the numbers 0, 1, 2, ….9, such that: Repetition is…

A: There are 10 digit available from 0 to 9. To construct a 5 digit number , the first digit always…

Q: In a particular lottery, 8 winning numbers are drawn from a group of 53 numbers. The order that the…

A: Total numbers of lotteries are 53. The total winning number are 8.

Q: . How many numbers of 5 different digits can be made from the digit 1,2,3,...9? 2. How many numbers…

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Q: A person ordering a certain model of car can choose any of 9 colors, either manual or automatic…

A: A person is ordering a car, such that  there are 9 possible ways to choose colors, two ways to…

Q: How many different ways can you arrange 3 letters {T, S, U} such that repetition is allowed and the…

A: Permutation: A permutation is defined as the ways in which objects canbe arranged.There are two…

Q: How many words can be formed by permutation of the letters of the word DEPRESSION such that each…

A: Given word DEPRESSION We have to calculate No. Of words such that obtained word does not contain 2…

Q: There are 5 boys and 4 girls. How many different ways are there to arrange these 9 persons in a row…

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Q: Suppose we want to choose 2 colors, without replacement, from the 5 colors red, blue, green, purple,…

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Q: Suppose we select 3 students randomly out of a class of 10 students to read a paper from the…

A:

Q: How many different phone numbers can be formed if it must have 7 digits and cannot start with 0 or 1…

A: Given data: phone numbers can be formed if it must have 7 digits and cannot start with 0 or 1 and…

Q: A lottery game requires that you pick 7 different numbers from 1 to 77. If you pick all 7 winning…

A: We have to find the no  of ways given as:

Q: How many different 3-digit numbers are possible using only the digits 1,5,6,7,8 ? How many…

A: We have to find no of ways for make 3 and 4 digit numbers  when repetition allow and not allowed

Q: A group contains n men and n women. How many ways are there to arrange these people in a row if the…

A: It is given that the group contains ‘n’ men and ‘n’ women.

Q: set of two - digit numbers obtained from the digits 1

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Q: A lottery game requires that you pick 7 different numbers from 1 to 59. If you pick all 7 winning…

A: According to the combination rule, if r distinct items are to be chosen from n items without…

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: How many three-digit numbers can be constructed from the digits 0, 3, 4, 5, 6, 8, 9 if: a)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: How many different 3-digit numbers are possible using only the digits 6,7,8,9 ? How many…

A: Given, There are 4 digit, 6,7,8,9

Q: Show that you can arrange n copies of all 3" ternary strings so that two consecutive strings differ…

A: Given that there are 3n ternary strings. Ternary strings consist of only three numbers either 1, 2,…

Q: Suppose we want to choose   7 colors, without replacement, from   9 distinct colors. How many…

A: Solution: From the given information, 7 colors without replacement should choose from 9 distinct…

Q: You are burning a CD for your assignments. You have assignments of 15 different However, you want to…

A: Determine the number of orders that can be put 7 of the 15 assignments onto the CD. The number of…

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: How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5 if the…

A: Total numbers 0 , 1 , 2 , 3 , 4  5 = 6

Q: How many three-digit numbers can be constructed from the digits 0, 1,2,3,4,5,6,8,9 if the number…

A: Given digits is0, 1, 2, 3, 4, 5, 6, 7, 8, 9Total no.of digits=10

Q: 8. Find the number of different salads consisting of one or more of these vegetables – Tomatoes,…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: How many ways are there to select 5 cookies from a jar containing 3 types when repetition is…

A: Theorem-  there are C(n+r-1 , r) ways of choosing r-combination from a set of n elements when…

Q: In how many ways can 7 Math Teachers be employed from 10 male and 6 female applicants? A florist…

A: 1.Total number of applicants are 10+6=16. The number of applicants to be employed are 7. Then, the…

Q: We are making 5-letter words from the set of letters a, b, c, d, e, f..., in such a way that we have…

A: Here we will use permutation /arrangement and combination / selection  Number of way r object can be…

Q: 20 different comic books will be distributed to 5 kids. 1) How many ways are there to distribute the…

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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.