Find a conjecture about each pattern  J, F, M, A, M, J, J,A , _ , _ , _

Q: How many permutations of a set five distinct objects taken three at a time are there?

A: Given:-                 How many permutations of a set five distinct objects taken three at a time…

Q: 3. Find the number of distinct permutations that can be formed your ID number.

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Q: What is/are the mode(s) of this group of numbers? (4, 6, 9, 5)

A: Mode: Mode is the value, which has the highest frequency among all other values of the observation.

Q: (BUA)NC

A: B∪A∩C' In this B∪A represents all the portions icluding A and B.  So, the venn diagram can be drawn…

Q: Venn diagrams show

A: Given that: Venn Diagrams

Q: In a survey conducted on 64 sportsmen, it was realized that 30 of them play football, 30 play…

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Q: Which notation is correctly describe the Venn Diagram?

A: Let A be a set, then the complement of set A is denoted as A'. It can be written that A'=U-A, where…

Q: How many permutations of the letters A, B, C, D, E, F, G are there in which the three letters ABC…

A: Given letters are : A, B, C, D, E, F, G. and it is given that three letters A, B and C appears…

Q: A combination is a selectio objects from а. n objects

A: Combination is a technique which represents the number of possible outcomes from n objects

Q: Let A = {1,2, 3, 4}, R = {(1,1), (1,2), (1, 4), (2,1), (3,3), (4, 1), (4,4)}. Draw a diagraph and…

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Q: Let V = { a, e, i, o, u } andB = { a, i, k, u}. Find V – B and B – V

A: V-B= elements those lie in V but not in B  Hence, V-B={e,o}

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: Consider the sets: U = {a,b,c,d,e,f,g,h,I,j,k}; A = {a,b,c,d,e}; B={a, d, e, i}; C= {d,e,f,g,k}…

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Q: How many subsets of S do not contain any upper case letters?

A: given set S=A,B,a,b,c,d,1,2,3,4 claim- to find how many subsets of Sdo not contain any upper case…

Q: Can you give me an example of What is Permutations Rule (when all of the items are different?

A: Permutation rule:There are n different items and r number of selections and the selections are made…

Q: Find the set A nB. U= {1, 2, 3, 4, 5, 6, 7} A= {1, 2, 3, 4} B= {1, 2, 5}

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Q: Determine the number of ways in which the four corners of a squarecan be colored with two colors.…

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Q: 6. Show that for n attributes A, A2, A3, ..., An (A, Az Az ... A, ) > ( A, ) + ( A2 )-(A3) + ... + (…

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Q: Consider selecting two elements, a and b, from the set A = {a, b, c, d, e}. List all possible…

A: All possible subsets having 2 elements of given set A ={a,b,c,d,e}  Are given below

Q: Let A = {5, 6, 7,9}, B = {x € N|x is odd} , C = {1,2, 3, 4, 5, 6, 7, 8, 9}. Show that A B and ACC.

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

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Q: Number theory

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Q: Show that if there are 8 people in a room, then at least two of them must have been born on the same…

A: There are 7 days in a week.  So we can have 7 people who can have different birthdays from Sunday to…

Q: How many permutations of {1,2,3,4,5,6,7} have exactly one element fixed?

A: Using inclusion-exclusion principle to compute the given permutation: There are 71·6! ways to select…

Q: Find the number of distinguishable permutations of the group of letters. Z, V, C, C, V, C, C, V, M,…

A: Letter   Frequency---------  ----------Z                1V                4C                4M…

Q: lowing symbols are part of the

A: 0,1,6 are derived from Hindu Arabic system

Q: Each character in a password is either a digit [0-9] or lowercase letter [a-z]. How many valid…

A: There are 10 digits as 0,1,2,3,4,5,6,7,8,9 and 26 letters, which are “ a, b, c, d, e, f, g, h, i, j,…

Q: Let A = { a, e, i, o, u } and B = { a, i, u }. Show that A ∪ B = A

A: A ∪ B ={ a, e, i, o, u } ∪ { a, i, u }           = { a, e, i, o, u }          = A

Q: State whether each arrangement represents a permutation or a combination.   a. 8 people seated…

A: Arrangement classification- Permutation or Combination

Q: partition of Z into four subsets.

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Q: 8. If u = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {2, 3, 5, 8} and B = {0, 3, 5, 7, 10}. Then…

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Q: Show that AU (B n C) = (C U B)n Á using Membership Tables.

A: Form the membership table for A∪B∩C as follows.

Q: onsider the following tree Descendent of e, r and n Siblings of d, c, and u Ancestor of s, c and a

A: Given tree is

Q: Each character in a password is either a digit [0-9] or lowercase letter [a-z]. How many valid…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: Each character in a password is either a digit [0-9] or lowercase letter [a-z]. How many valid…

A: Given: Each character in a password is either a digit [0-9]  There are 10 digits as…

Q: andomly selected from a

A: we have given a sample of 6 measurements was randomly selected from normally distributed population…

Q: er

A: To find all the permutations of the 4 objects a ,b, c, and d, taken 3 at a time.

Q: Find the number of distinguishable permutations of: 5 As, 3 Gs, and 4 Ns

A: The answer is, 27720   The detailed solution is as follows below:

Q: Assume that a fair die is relled. The samnple space is1, 2, 3, 4, 5, 6| and all the outcomes are…

A: If a fair die is rolled, then we get sample space as  S={1,2,3,4,5,6} Let E denote the outcome of 6…

Q: Find the number of distinguishable permutations of the given letters "AAABBBCCC".

A: The given letters are "AAABBBCCC".

Q: Find the number of distinguishable permutations of the given letters "AABBCC". Your answer is:

A:

Q: Find the number of distinguishable permutations of the given letters "AABBCC". Your answer is :

A: Soln :- Number of distinguishable permutations of the letters "AA BB CC "There are total 3 different…

Q: Prove that among any group of people, there are always two people with the same number of friends…

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Q: Draw the tree diagram giving the permutations of {x, y, z, u} objects.

A: Permutation determines the number of possible arrangements in a set when the order of the…

Q: a. Assuming that 2 of the ages are randomly selected with replacement, list the different possible…

A: We have 3 ages given, i.e, 55,46 and 60. Two ages are randomly selected with replacement, which…

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: Define subsets and give a relevant example along with it.

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Q: by each participant is presented here.

A: Let X1 be the random variable such that jail sentence recommended by the participants in group 1. M1…

Q: Find the set A UØ. U= {1, 2, 3, 4, 5, 6} A=(3, 4, 5, 6}

A: Given, U=1, 2, 3, 4, 5, 6, A=3, 4, 5, 6