Let S = {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} a. How many subsets are there total? 4096 b. How many subsets have {2,3, 5} as a subset? 512 c. How many subsets contain at least one odd number? 4032 d. How many subsets contain exactly one even number? 4032

Q: A class has 28 students. In how many different way can four student form a group for an…

A: GivenTotal no.of students in a class(n)=28No.of students form a group for an activity(k)=4

Q: 12. How many 5-digit numbers are there in which three of the digits are 7, or two of the digits are…

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Q: 3. Let, a, 3, a2 = 4 and for n 2 3, a, =

A: In the given question, the solution of recurrence relation is used. Recurrence Relation A recurrence…

Q: Suppose U = {1,2,3,4,5,6,7,8,9,10}, A = {2,4,6,8,10}, and B = {2,3,5,7}, which values are in A…

A: We have given that,  U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } A = { 2, 4, 6, 8, 10 } B = { 2, 3, 5, 7 }

Q: List all the combinations of 6 objects 1, 2, 3, 4, 5, and 6 taken 3 at a time. What is C(6, 3)?

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Q: if A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7} what is A n B?

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Q: In how many ways can 12 people line up in a row? 144 O 12 O 1212 479,001,600

A: Multiplication rule: If there are a ways of doing something and b ways of doing another thing, there…

Q: he word "Knickknack" if "nack" goes together in a

A: Given: Total number of letters = 10  Number of letters to be together = 4 Number of 'k' apart from…

Q: In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a…

A: We can interpret this question as how to split seven students into groups of 3, 2 and 2.

Q: Suppose 15 cars start at a car race. In how many ways can the top 3 cars finish the​ race? The…

A: Permutations: The number of permutations of r items selected from n items is, Prn=n!n-r! In this…

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

A: Concept: Since, in every case first letter shoud be G, X, P, or L.  Hence, total number of ways for…

Q: 1. Let S = (1,2,3, 4, 5, 6} (a) How many subsets are there total? (b) How many subsets have {2, 3,…

A: Hello! Thank you for the question but as per our honor code, we'll able to solve only the first…

Q: 3. How many 3-digit numbers are there that are divisible either by 5, 7 or 9?

A:

Q: O 4: O 1: nchroom has 12 tables and 108 chairs. tables : chairs

A: There are 12 tables and 108 chairs in a lunchtable. The ratio of tables and chairs,…

Q: 9. How many ordered sets of 3 even numbers are there that will add up to 60? How many different ways…

A: Combinations: The combination is a mathematical method that determines the number of possible…

Q: IV How many different number plates for cars could be made if each number plate contains four (4) of…

A: Hi! Thank you for the question As per the honor code, We’ll answer the first question since the…

Q: a) How many different license plates are possible if each contains 2 letters​ (out of the​…

A: We solve this question by using permutations If characters are not repeated then the total number of…

Q: 3. In how many ways can you arrange 5 books on a shelf from available 10?

A: The number of all combination of n things, taken r at  time is given by:

Q: How many 4-digit numbers can be formed from 0, 1, 3, 5, 7, & 9 if repetition of digits is NOT…

A: Solution-: How many 4-digit numbers can be formed from 0,1,3,5,7 and 9 if repetition of digits is…

Q: The digits 0, 1, 2, 3, 4, 5, 6 and 7 are used to make 4 digit codes. (a) How many unique codes are…

A: As per Bartleby guideline, if more than three subparts are asked only first three to be answered…

Q: 10(c) Suppose a set of 8 numbers are selected from the set {1,2,...,13,14}. Show that two of the…

A:

Q: Pick ২ se+ S = } \, 2, ..., n} S= {\,2,..., h} of

A: The given information is: S=1, 2, 3, 4, 5...   ,nT=∑iXi         ,   i∈S

Q: How many distinguished permutations of the set of letters, {a,b, c, c, d, d, d} can be formed.

A: Given that, {a, b, c, c, d, d, d} a = 1 b = 1 c = 2 d = 3

Q: Which set is equal to the set B={8,74,347,9,100}?

A: If two sets A and B are said to be equal then the number of elements in both set should be same.…

Q: Q3/ How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 such…

A:

Q: In how many different ways can 9 people arrange themselves in a line to receive service from a…

A: Given information: There are total 9 people arrange themselves in a line to receive service from a…

Q: If A={2,4,6,8,10,12,14} and B={1,3,6,9,12,15,18,21}. Find A∪B.

A:

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

A:

Q: Let ā = [-2, 3, 5], b = [4, –1, 4] and č = [8, - 6, 1]. Calculate (3č + 45) • (ā + 5):

A: Option A is Correct Answer. i.e., 207

Q: Suppose there are 200 students in a class. How many ways to select 30, 31 or 32 students from the…

A: There are 200 students in a class.

Q: Let S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Suppose six integers are chosen from S. Must there be two…

A: Consider the following given set:S = {3,4,5,6,7,8,9,10,11,12}Suppose six integers are chosen from…

Q: Suppose a group of twelve (12) people consists of five (5) men and seven (7) women. How many…

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Q: How many 3-digit numbers with no repeated didgits using 4,5,6,7,8 can be a) Less than 520 b) Greater…

A: (a)given digits are 4,5,6,7,8.     Number of digits = 5 ; for the formation of 3 digit numbers from…

Q: Let S = {1,2,3, 4, 5, 6, 7, 8, 9, 10, 11, 12} a. How many subsets are there total? 4096 b. How many…

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

Q: (e) How many integers are there from 1,0 through 9,99 (b) How many odd integers are there from 1,000…

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Q: 1. Let S = {1,2,3,4,5,6} (a) How many subsets are there total? (b) How many subsets have {2,3,5} as…

A: Given set,

Q: How many ways can a set of 10 different books be arranged on a shelf if they are not in alphabetical…

A:

Q: How many ways can a set of 10 different books be arranged on a shelf if they are not in alphabetical…

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Q: A computer programming team has 13 members. Suppose seven team members are women and six are men.…

A: Solution: From the given information, the programming team has 13 members. Among them 7 are women…

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: Given S = { – 2, 4.2610, 2, e, 4, – 6.41026...., 6, 2.13210...., 10, 7} The subset consisting of all…

A:

Q: How many different 10-letter words (real or imaginary) can be formed from the following letters? X,…

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Q: A class has 35 students. In how many different ways can five students form a group for an​ activity?…

A: It is given that N is 35 and r is 5.

Q: For n attributes A,, A2, --. , An (A, A2 . An) 2 (A,) + (A2) + .. + (A,)- (n - 1)N Where N is the…

A: To show that, For n attributes A1, A2,..... , An. (A1, A2,..... , An) ≥ (A1)+(A2)+...+(An)-(n-1)N…

Q: a. How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit…

A: Part (a) Calculate the number of three digit numbers formed using the letters 0,1,2.3,4,5,6. The…

Q: Eighteen persons have first names Ali, Bahar, and Carlie and last names Daud and Elyas. Show that at…

A: According to pigeonhole principle it is known that, if there are n pigeons into k pigeon holes,…

Q: How many subsets are there of the set N = {8, 43, 68, 15, 34}

A: We need to find number of subsets for a given set N

Q: If repetitions are not allowed, how many three digit numbers formed with the digits 0, 1, 2, 3, 4,…

A: Topic = Permutation and combination As per guidelines , at a time only three sub-parts of a question…

Q: A four-digit number is to be formed from the digits 0, 1, 2, 3, 5, 7, 8, and 9. How many four-digit…

A: Given digits is 0,1,2,3,5,7,8,9

Q: 3. How many three digit numbers can be formed from the set 0, 1, 2, 3 .........9 if repetitions are…

A: Here Given Digits  Total Number=10 Here we will use Combination Method for Counting..