There are 26 letters in the alphabet. How many are there of each of the following? (a) Sequences of letters of length 5? (b) Sequences of letters of length 5, with no repeated letters? (c) Sets of letters of size 5?

Q: how many length twenty strings of a's, b's, and c's have ten a's, six b's, and four c's

A: 20!10!×6!×4! in which 20 is used for total string length.  10 for a's and   6 for b's , 4 for c's

Q: In how many ways can you select two books to read from a shelf of ten books? (Order is important.)

A: Given thatr = 2 n = 10

Q: How many four letter sequences are possible that use the letter a,b,c and d once each. ????

A: We have four different letters a, b, c and d. Our aim is to find the number of all possible…

Q: Three men and three women are to be seated in a row of chairs numbered 1 through 6. (a) How many…

A: When n people are arranged in a line it can be arranged by n!

Q: How many seven-digit numbers can be formed with the first two digits odd and the last five digits…

A: The total number of digits from 0 to 9 is 10.

Q: 11: Find the sum of the first 22 terms of the AP : 8, 3, -2, . .

A: Sum of first n terms of a Arithmetic Progression with first term a and common difference d is  Sn =…

Q: How many numbers of four digits can be formed with the digits 0, 1, 2, 3 (repetition of digits being…

A:

Q: How many ways can 6 ladies be seated in a circular table such that 2 of the ladies must always sit…

A: To find: The number of ways to arrange 6 ladies in a circular table such that 2 of the ladies must…

Q: how many sequences of 2n letters can be formed using n distinct symbols if each symbol is used…

A:

Q: How many three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters (a) is…

A: Given5 letters is "FGHIJ"No.of letters = 5

Q: A company has 10 different warehouses for storing their inventory. They will be storing 100…

A: Given:-             A company has 10 different warehouses for storing their inventory. They will be…

Q: A drug is effective in nine cases out of ten. If it is tested on 12 patients, what is the…

A:

Q: In how many ways can 5 persons be seated in a room where there are 10 seats?

A: We have to find number of ways to seat people in room.

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: How many different ways can the letters of "jogging" be arranged? The number of different ways that…

A: The word “jogging” contains a total of 7 letters in which “g” letter is repeated 3 times.

Q: How many different sequences of 5 ternary digits (0, 1, 2) are possible? The number of different…

A: There are total 3 choices for each digit. We will have to pick 5 digits. Each digit can be picked in…

Q: How many ways are there to arrange the letters in COMPANIES? (a) with vowels in alphabetical order?…

A: a) There are total number of ways to arrange letters in alphabetical order is 9!. Here four vowels…

Q: How many 7-digit telephone numbers are possible if the first digit cannot be four and (a) only odd…

A: Total digits :  0,1,2,3,4,5,6,7,8,9  7-digit telephone numbers= ?  First digit can not be 4

Q: This is a mathematics question. There are 8 numbers in a sequence that add up to 250 (ex.…

A: The details are given as step 2.

Q: How many five​-digit numbers can be formed with the first two digits odd and the last three digits…

A: The number of digits need to be formed is five. The first two digits are odd and the last three…

Q: How many ways are there of arranging the 26 letters of the alphabet so that none of the words be,…

A:

Q: How many possible ways can the top 5 finishers come in during a race with 24 racers? Each place…

A: This is a permutation problem.   Out of the 24, there will be 5 racers in the top 5.

Q: A ternary digit is either 0, 1, or 2. How many sequences of nine ternary digits are possible…

A: The ternary digit is either 0 or 1 or 2.

Q: How many four letters code words are possible using the letters in COIN, if (i) the letters may not…

A:

Q: Many banks require customers who use the automated teller machine (ATM) to enter a four-digit…

A: ATM machine needs four digit password before transaction.  digits : {0,1,2,3,4,5,6,7,8,9} digits can…

Q: There are 10 questions in a final ėxamination for Discrete Mathematics. Each question is assigned at…

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Q: How many numbers can be made each using all the numerals in the set S = {1,2,2,3, 3, 3, 0}

A: According to the provided information, The set are S= {1, 2, 2, 3, 3, 3, 0}

Q: As of April 2006, roughly 50 million.com web domain names were registered (e.g., yahoo.com). (a) How…

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

Q: n crayon box contains 2 green, 3 yellow and 4 blue crayons. In how many ways can one choose 3…

A:

Q: How many six-lettered words starting with the letter T can be made from all the letters of the word…

A: