1. Consider the set A = {a,b,c,d,...,x,y,z} of the 26 letters os the alphabet. Determine the total number of sequences with 5 letters that can be formed such that the 1st and the last letter are distinct vowels and the remaining letters are distinct consonants

Q: 2. How many different 6 letter strings can we make with only the letters J, E, R, M, Y, given the…

A: We have to use proper permutations and combinations.

Q: How many six-letter “words” (sequences of letters with repetition) are there in which the first and…

A: We have to find how many six letters are to be formed with repetition in which first and last letter…

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 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: How many eight-letter "words" (sequences of letters with repetition) are there in which vowels…

A:

Q: How many ordered sequences are possible that contain four objects chosen from thirteen?

A: According to the given information in this question We need to find the value P( 13,4)

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: 3. (8 points) a. How many arrangements in a row of two or three letters can be formed using the…

A: The objective of the first part of the question is to find the number of arrangements of two or…

Q: In how many ways can the letters of the word 'RETAIL' be arranged in such a way that the vowels…

A: The objective is to find out in how many possible ways can the letters of the word 'RETAIL' be…

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

A:

Q: A. Compute the total number of sets (of size 5) containing exactly 2 elements from X and 3 elements…

A:

Q: 3. (8 points) a. How many arrangements in a row of two or three letters can be formed using the…

A: The objective of the question is to find the number of possible arrangements of the letters in the…

Q: How many ways are there to select three unordered elements from a set with five elements when…

A: Given: Number of elements = 5 Number of unordered elements = 3 If repetition is allowed,…

Q: If strings of 3 letters are formed using the letters R, S, T, U, V, W how many such words are…

A: The objective of this question is to calculate the number of possible 3-letter words that can be…

Q: A warehouse tracks inventory using stock codes consisting of a sequence of 5 uppercase letters…

A:

Q: In how many ways can 7 children and 6 mother be arranged in a row so that:  No two children are sit…

A:

Q: Q4) Let A = {1,2,3,4} be the given set. Find 1. п(Р(A)) 2. Write power set, P(A) 3. Write a class…

A: Given set is  A={1,2,3,4}

Q: Find the number of words of length n using the alphabet {a, b, c, d, e} in which the total number of…

A:

Q: How many strings of length 5 can be formed if the alphabet (set of available characters)is {a,b,c}…

A: The given alphabets are {a, b, c}. So, the number of characters is 3. The length of the string is 5.

Q: How many 4-letter strings of upper- and/or lowercase letters are there that contain at least two…

A: To determine the number of 4-letter strings of upper and /or  lowercase letters are there that…

Q: Let S={1,2,3,4,5,6,7,8,9,10,11}   How many subsets contain at least one odd number?

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Q: A multiset is a collection of objects, just like a set, but can contain an object more than once…

A:

Q: In how many ways can the letters in the word sequences be arranged if the first letter must be Q?

A: There are 9 letters in the word sequences.   Letter Frequency s 2 e 3 q 1 n 1 c 1 u 1…

Q: Recall that hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A,…

A: We know that,Hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,…

Q: Find the number of ways that the numbers 1, 2, ..., 12 can be arranged in a sequence…

A: Observed that each sequence contain 1st 6 elements in descending order and remaining 6 elements in…

Q: How many ordered sequences are possible that contain eight objects chosen from eleven?

A: Given that, Total objects = 11 Order matters

Q: Suppose that a1, a2, a3, . .. is a sequence of sequences of zeros and ones. aj is a11, a12, a13, ·…

A: