Consider Set A = {a,b,c,d,,x,y,z) of the 26 letters of the alphabet. Determine the total number of sequences with 5 letters that can form so that the first letter and the last letter are vowels other letters are all different consonants.

Q: An oil company is going to issue new ID codes to its employees. Each code will have one letter,…

A: We have given that We have 22 letters (expect W,X,Y,Z) And 10 digits

Q: How many outfits can be made from 4 pairs of slacks, 5 shirts, and 3 ties, if one selection from…

A: First decide on a pair of slacks.For that there are 4 different choices.Now for each of those…

Q: We are making 8-letter words from the set of letters a, b, c, d, e, f ..., in such a way that we…

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

Q: How many strings of length two can be formed by using the letters A, B, C, D E and F without…

A: Given letters, A, B, C, D, E, F We have to find number of strings of length two

Q: How many different ways can seven people sit in a row in the last four seats at the concert?( the…

A: There is total 7 people and four seats.

Q: How many distinct 5-letter strings can be created using the letters A, B, C, D, E if repetition is…

A:

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: in how many different ways can 7 potted plants be arrangesd in row

A: We can arrange n things in n! ways in a row.

Q: 2 letter sequences can be formed from the 8 letters in theword “sequence”?

A: Given, A letter = [ s,e,q,u,e,n,c,e] Number of letters = 8 By using  permutation and combination,…

Q: Suppose a set of 8 numbers are selected from the set: {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}…

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Q: My first car had a license plate which had 3 letters followed by 3 digits. How many different such…

A: We have to find different licenses plates.

Q: How many six-person lineups can be formed from a 10-player volleyball roster? (Every player plays…

A: There are 6 places that has to be filled by 10 players and any player can choose any position.

Q: Use any method, list all the three digit numbers from the set {3,4,5,6} where there are no repeating…

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Q: same

A:

Q: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

Q: How many 15 letter strings containing only a's, b's, and c's have 6 a's and 4 b's?

A: Given: 15 letter strings containing only a's, b's and c's

Q: Suppose you have ten blocks with the letter A, A, C, E, E, E, R, S, S, and T. How many ways can we…

A: 10 blocks with letters :  A, A, C, E, E, E, R, S, S, TNumber of ways to order all 10 blocks = ?

Q: Draw an ordered stemplot of these scores: 22, 32, 34, 30, 28, 19, 26, 18, 19, 20. List the 'leaves'…

A: Ordered data x 18 19 19 20 22 26 28 30 32 34

Q: A bank of 9 movies is chosen from for a movie marathon in which 3 movies will be played in a…

A: Given that,  There are 9 movies in the bank. According to the given condition, 3 movies are played…

Q: Find the number of different ways that a family of 9 can be seated around a circular table with 9…

A:

Q: How many outfits can be constructed with 1 shirt, 1 pants, and 1 tie from a wardrobe of 2 shirts, 5…

A: The given problem is based on combination {Because order doesn't matter}. The combination of…

Q: Suppose that there are 9 female and 12 male students in a classroom. How many different 5-member…

A: According to the provided information, number of female students = 9 number of male students = 12…

Q: A standard deck of cards has 52 cards. There are four suits: ♥, ♦, ♣, ♠. For each suit, there are…

A: Conditions:• The first group has three cards of the same denomination.• The second group has three…

Q: 14 different letters of alphabet are given, words with 6 letters are formed from these given…

A: There are 14 different letters. We will make words with 6 letters.  So there are 146=7529536 ways to…

Q: Certain automobile license plates consist of a sequence of three letters followed by four digits. If…

A: We have a license plate that consists of a sequence of three letters followed by four digits. The…

Q: When ordering a certain type of computer hard drive choices of monitor. In how many ways can a…

A:

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: 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: Suppose that there is a bag containing 6 marbles. How many ways can you draw 4 marbles from the bag…

A: The bag contains =6 marbles number of marbles drawn=4

Q: How many distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2 orange marbles…

A: Given problem:- How many distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2…

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

A:

Q: In an apartment complex with 10 mailboxes, in how many ways can a mail carrier distribute 10 letters…

A: The formula for finding the  one addressed to each box such that at least one letter is put into the…

Q: A product code consists of a string of 4 different letters selected from the set {S,T,U,V,W,X}. How…

A: The number of ways to arrange r objects selected from n distinct objects is given by the permutation…

Q: How many different selections of three books can be made from a set of fifteen books?

A: Introduction:According to the permutation rule, if r distinct items are to be chosen from n items…