) How many 5 letter code words can be made with the first 7 letters in the alphabet (i) if no letter can be repeated?  (ii) if no adjacent letter is the same?

Q: How many permutations are possible with the letters TENNESSEE? If a student is to answer any 6…

A: Permutation is how many different ways are there for arranging n objects in r objects. where n>r…

Q: How many ways can the letters of the word PROMISE be arranged so that the vowels always come…

A: Given word is PROMISENumber of vowels in word PROMISE…

Q: A machine puts out 16 imperfect articles in a sample of 500. After the machine is over-hauled, it…

A:

Q: In how many ways can a  friend visit his 3  friends  if he must visit all of them in a single day

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

Q: A fair coin is tossed 5 times and the sequence of heads and tails is observed. How many outcomes…

A:

Q: In how many ways can 10 distinct books be divided among three students if the first student gets…

A: Solution: From the given information, there are 10 distinct books divided among 3 students. First…

Q: A Certain bacteria culture triples in a number every day. If there were 100 bacteria at the end of…

A: Let in general there are n0 bacteria after 1 day.  Then after second day, no of bacteria will be 3a0…

Q: To gain access to his account, a customer using an automatic teller machine (ATM) must enter a…

A:

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: In how many ways can first, second, and third prizes be awarded in a contest with 210 contestants?

A: There are a total of 210 contestants. Remember that the same person cannot receive more than 1…

Q: 1) There are 480480 people in attendance for the conference. If every person shook hands with every…

A: Hello. Since your question has multiple parts, we will solve the first three parts for you. If you…

Q: Current rules for telephone area codes allow the use of digits​ 2-9 for the first​ digit, and​ 0-9…

A:

Q: a. In how many ways can the letters of the word 'CORPORATION' be arranged so that the vowels always…

A: here use counting principle

Q: 1. How many ways are there to choose a dozen donuts from 18 varieties: a) if there are no two donuts…

A:

Q: how many different ways can the letters of the word wombat be arranged if the letters wo must remain…

A: Using Permutation and Combination we can solve for different ways

Q: (1). How many different words (including nonsense words) can you make by rearranging the letters of…

A: 1) The given word is “EFFERVESCENCE”. The total number of letters is 13. There are 2 C’s, 5 E’s,…

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

A: Given: A contractor builds homes of 9 different models and presently has 3 lots to build on.

Q: How many 5-digit numbers can be formed using the digits 0 to 9 if repetitions are allowed?

A: Total number of digits allowed are : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,

Q: how many different ways can the letters of the word JOYRIDE be arranged such that all letters are…

A:

Q: How many different 7-letter words can be made a. if the first letter must be B or X and no letter…

A: Let m choices to be made with n1 options for the 1st choice, n2 options for the 2nd choice, … , nm…

Q: In how many ways can a person select seven party guests from 12 women if he is to avoid having a…

A:

Q: a. If there are 8 different colors of foot balls are available in a sports shop, in how many wavs…

A:

Q: How many different 7-letter words can be made a. if the first letter must be B or X and no letter…

A:

Q: A user’s password to access a computer system consists of three digits and two letters.…

A: A permutation of a set is an arrangement of its members into a sequence or if the set is already…

Q: How many 5-digit license plate numbers can we generate from the numbers, 0, 1, 2, 3, and 4 if it…

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: In how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10…

A: Given that the picture has to be taken for 6 people out of 10 where exactly one of the bride or the…

Q: In how many ways can a person invite 4 out of their 13 closest friends to a dinner party?

A: Here there are 13 friends out of which the person has to invite 4 friends for the dinner party. Here…

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: How many different 5​-letter radio station call letters can be made a.  if the first letter must be…

A: Let m choices to be made with n1 options for the 1st choice, n2 options for the 2nd choice, … , nm…

Q: License plates in a particular state are to consist of 3 digits followed by 2 uppercase letters. How…

A: no.of digits=10  (0 to 10)no.of uppercase letters=26   (A to Z) 9 ways fill it (0 , 2, 3...10) 9…

Q: Customer account "numbers" for a certain company consists of 22 letters followed by 44 single-digit…

A: In general, the number of digits is 10. They are, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Q: 1. A student must answer 3 out of 5 easy question on the test. In how many ways can a student select…

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

Q: How many 5-digit numbers can be made from the digits 1 to 9 if: a) Repetition of digits is allowed?…

A: Here AS PER POLICY I HAVE CALCULATED FIRST 3 SUBPART ONLY

Q: (a) If repetition of digits is not​ allowed, how many four​-digit numbers can be formed using the…

A: Solution: a. The given digits are 1, 2, 3, 4 and 5. Here, the repetition is not allowed.

Q: In how many ways can 7 male students be arranged in a row if Hanz and Fitch insist next to each…

A:

Q: How many 4-digit pin codes can be made using the numbers 0 up to 9 if repetition is not allowed and…

A: Solution Total number of digits from 0 to 9 = 10

Q: ny three-letter "words" can be made from 6 different letters "FGHIJK" if... a) Repetition of…

A: The fundamental counting principle says that if n ways are there to complete one thing, and m ways…

Q: How many strings of eight English letters are there a) that contain no vowels, if letters can be…

A: Given the question that, How many strings of eight English letters are there- a) that…

Q: How many permutations are there in the letters of the word COMMOTION if the first and last letters…

A: Given :   C 0 M M O T I O N if first and last must either be C or N , there are two ways…

Q: How many 5-digit numbers can be formed using the digits 2, 3, 4, 5, and 6 without repetition? With…

A: To find how many   5 digit number  can be formed using  2,3,4,5 and 6 without  repetition and then…

Q: How many ways are there to divide a red bracelet, a yellow bracelet, a green bracelet, and a black…

A: It is given that there is 4 different coloured bracelets, a red, a yellow ,a green and a black and 4…

Q: In how many ways can a person select seven party guests from 12 women  if he is to avoid having a…

A: Here we will use the concept of Combination

Q: How many permutations are there of the letters in the word 'CHARGES', if all the letters are used…

A: The formula for Permutation is nPr = n!/(n – r)!.

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: To use an automated teller machine at a certain bank, you must enter a 5-digit code, using the…

A: To use an automated teller machine at a certain bank, we have to enter a 5 digit code using digits…

Q: How many six-number combinations can be generated from the numbers from 1 to 42 inclusive, without…

A: Given information: A 6 number combination is to be generated. The possible numbers are selected…

Q: 1.How many different four-letter passwords can be formed from the letters A, B, C, D, E, F and G if…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…