4. Give the 100th and the nth entries for these lists, assuming the patterns continue. A) 4, 6, 8, 10, 12, ... 100th nth | ber in B) 1, 4, 9, 16, 25, 36, .. 1, the 100th nth 100th nth 100th nth D) 4, 7, 10, 13, ...

Q: How many subsets are there of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}? How many of these subsets are proper?

A: Let the given set is A, having elements as

Q: How many ways are there to form a subset of [n] of size k with the property that each selected…

A: Given n=8 k=3 4 ways 1,4,7,1,4,8,1,5,8 and 2,5,8 Find How many ways are there to form a subset of n…

Q: 2. Civil Engineers at a large convention are offered 6 construction tours on each of 3 days. In how…

A: Given : Number of tours = 6 Number of days = 3

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

A:

Q: For the Venn diagram in Figure 2.4, suppose U = {integers}, N = {1, 2, 3, ...}, P = {p: p is prime},…

A: U=IntegersN=1,2,3,4,‐‐‐P=P:P is prime=2,3,5,7,11,13,17,19,23,‐‐‐F=1,2,3,5,8,-1,-2,-5

Q: Suppose there were 600 nurses graduating this year.  Assume that 400 were registered nurses (RN),…

A: Need to complete venn diagram

Q: 5. How many 2-permutations are there of a set of eight objects?

A: We know that,  The formula pf permutations is,  nPr = P(n, r) = n!/(n-r)!

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: Show that if one event A is contained in another event B (i.e., A is a subset of B), then P(A) <…

A:

Q: Give the transpose of the permutation [2, 5, 1, 6, 3, 4], and find the number of inversions in both…

A: To find- Give the transpose of the permutation 2, 5, 1, 6, 3, 4, and find the number of inversions…

Q: 5. How many possible pemutations are there in the letters of the word PHILIPPINES?

A:

Q: A tree with 8 vertices has edges. O 28 O 7 O 9

A:

Q: 9. How many 8 element subsets are there in P({a, b, c, d, e, f, g, h, i, j, k, 1, m, n, 0, p})? 10.…

A: We have give a set of 16 elements. We have to get how many subsets which consists 8 elements.

Q: ifferent ways can the letters

A: To find :  To find different ways can the letters of the word 'JUDGE' be arranged such that the…

Q: 1. Out of 120 people, it was found that 50 like pasta, 42 like pizza, 39 like burger , 21 like pasta…

A:

Q: How many different words with or without meaning can be formed with the letters of the word…

A:

Q: A club has seven members. Three are to be chosen as a group to a national meeting. A) If the club…

A: Given Information:  Number of members in a group = 7  Number of men = 4  Number of women = 3

Q: 4. Suppose we impose a relation on the set of natural counting numbers, N = {1,2,3... }, such that R…

A: Given that the set N=1,2,3,.... and the relation R defined on the set N as follows:…

Q: How many 4-permutations are there of a set of six objects?

A:

Q: Number theory

A:

Q: How many subsets are there of the set N = {5, 42}?

A: We ahave to find no. Of subsets.

Q: a committe of 4 is to be selected from 6 men and 5 women. 1 particular man and 1 particular woman…

A: From the given information, there are 6 men and 5 women. That is, the total number of persons is…

Q: 1. How many 3-letter words with or without meaning, can be formed out of the letters of the word,…

A: 1. There are a total of 7 letters in the word 'MACHINE' If the repetition of letters is not allowed,…

Q: Use the pigeonhole principle to prove the following statement. For any gathering of six people,…

A: Two possibilities=&gt;( i )Mutual Friend                                  (ii)stranger  (let K be…

Q: Consider lists made from L, a, T, e, X, with repetitions allowed. How many 4-lists are there in…

A: Please refer to the image below.

Q: In the class of 50 students, 24 like Arabic, 21 like English and 18 like Mathematics 6 like Arabic…

A:

Q: Use pigeonhole principle 1. How many numbers must be selected from the set {1, 3, 5, 7, 9, 11, 13,…

A:

Q: one course only by using Venn diagram.

A:

Q: In how many ways can 8 books be choosen from a group of nine?

A:

Q: Suppose we want to choose 5 objects, without replacement, from 18 distinct objects. a) If the order…

A: Given,Total no.of distinct objects=18

Q: how many subsetsof one or more elemets can be formed from a set containing 12 elements?

A: Use concept of power set

Q: 1.A club with 15 members will choose 3 of them to attend a meeting. In how many different ways can…

A: Given that there are total 15 members and we will choose 3 of them. Since we will pick 3 persons in…

Q: How many ways can a group of n people be arranged in a circle that contains k equally distributed…

A: Number of ways of selecting k people from n people = Ckn = n!k!*(n-k)!

Q: How many ways are there to form a subset of (n| of size k with the property that each selected…

A: Let us define some events   A:- box 1 is selected B:- box 2 is selected E:- Yellow ball is selected

Q: 9, In a ceremony, out of 800 participants, 20 drank milk, 350 drank tea and 50 did not 520 drink any…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (a) How many 4-permutations are there of a set of six objects? (b) How many 2-permutations are there…

A:

Q: (a) How many 4-permutations are there of a set of five objects? (b) How many 2-permutations are…

A:

Q: how many distinct proper subsets are in N={10,49,70,19,37,56,26}

A: Assume two sets. Set A and Set B.Set A is the proper subset of set B if or only when set B contains…

Q: How many 3-letter arrangements can be formed if at least one of the letters is to be chosen from the…

A: Given  3-letter arrangements can be formed if at least one of the letters is to be chosen from the…

Q: in how many ways can we arrange the integers 1, 2, 3, 4, 5 in a line so that there are no occurence…

A: Answer is given in next step.

Q: in how many ways can we arrange the integers 1, 2, 3, 4, 5 in a line so that there are no occurence…

A: Given the integers 1,2, 3,4,5

Q: 11 How many 6-letter words (even without meaning) can be created from the letters of the word…

A: There are several powerful methods for counting objects and sets of objects without actually having…

Q: With no repetition allowed, 2-letter arrangements are to be made form E, B, O, N

A: Letters are E, B, O, and N. No repetition allowed. A)  2- letter arrangements are to be made. The…

Q: 2.21 Registrants at a large convention are offered 6 sightseeing tours on each of 3 days. In how…

A: Given: Number of sight seeing offered=6 Number of days of tour=3 Determine the number of ways in…

Q: How many possible unique deck orders can w • 1, 2, 3, 4, 5, 6, 7 to • 2, 6, 1, 7, 4, 3, 5 O 3 O 9 10…

A: Given numbers: 1, 2, 3, 4, 5, 6, 7.

Q: In how many ways can a large retail store select 3 sites on which to build a new store if it has 12…

A: We have to find given combination possible.

Q: Consider strings of lowercase letters. How many strings are there of lowercase letters of length…

A:

Q: n a survey of 120 people, it was found that: 65 read Newsweek magazine, 20 read both Newsweek and…

A: Given that:                     Total number of people = 120Number of people reading Newsweek…