A1,...,A13 are thirteen different subsets of {1,2,3,4,5,6,7,8,9,10}. If each Aj has 6 elements for all 1≤j≤13, show that you can find three numbers between 1 and 10 which belong to at least three subsets.

Q: List all the ordered arrangements of 4 objects 1, 2, 3, and 4 choosing 3 at a time without…

A: 4 objects are 1,2,3,4 If we have to choose 3 out of 4 (without repetition) Then, First object can be…

Q: Let the set B={−23,−16,−7,−2,20,36,48,72}. How many ways are there to choose a positive or an odd…

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Q: How many numbers greater than 3000 can be form with the digits 0,2,3,4 a.  if repetition is not…

A:

Q: Set A = | { 2, 2, 4, 5,1,2,6,9, 4, 5, 6, 2 } |. How many elements are in this set?

A: We have to find number of elements in set A

Q: Suppose a set of 8 numbers are selected from the set: {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}…

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Q: list all the subsets of  {1,2,∅}   and {{R}} R= real number

A: Number of subsets of a set with n elements is 2^n

Q: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

Q: How many permutations of the numbers (1, 2, 3, 4, 5, 6, 7, 8, 9} have the numbers 4, 5 and 6 in…

A: So, the numbers 4, 5 & 6 should remain at their natural position and the other numbers can…

Q: How many subsets are there of the set N = {9}?

A: Given,          The set is N=9We know that,         The number of subsets of a given set is 2n ;…

Q: set N = {9, 43, 66}?

A: Given that  Set N = {9, 43, 66}   We know that  The subsets possible are null set , subset of size…

Q: O Equal O Equivalent

A: Given: The set A=2, 4, 5, 8. The set B=2, 4, 6, 8. Two sets P and Q are said to to equal, if each…

Q: A combination of 3 balls are picked at random from a box containing 5 green, 4 white, and 3 black…

A: Hope this is useful.Thankyou

Q: Let W = {[ W is not 2a 46 : a, b ER ». Determine whether W is a subspace of R³. a subspace of R³…

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Q: Let A₁ = {1, 2, 3, 4, 5, 6}, A2 = {7, 8, 9, 10, 11, 12, 13} and {14, 15, 16, 17, 18, 19}. A3 = How…

A: Let A1=1, 2, 3, 4, 5, 6, A2=7, 8, 9, 10, 11, 12, 13 and A3=14, 15, 16, 17, 18, 19.   To Find: How…

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

A: We ahave to find no. Of subsets.

Q: How many elements are in the set {2,2,2,2}

A: We have to find number of elements

Q: There are 6 numbered balls in a bag. Each ball has a distinct number and the numbers are in {1,2, 3,…

A: Here given that there are 6 numbered balls in a bag. Each ball has a distinct number and the numbers…

Q: Let D (2,5,7}, E= (2,4,5,6) andF=(1,3,4,5,7). List the elements in the set (D UE)N F. (DUE)NF = }…

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Q: How many subsets are there of the set N = {6, 49}?

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Q: Suppose you have a set S= {1, 2, 3, 4}. How many ways can you arrange 2 elements of the set without…

A: Given   A problem on permutations. Please find the below attachment for clear explanation.

Q: Let T = {1, 2, 3, 4, 5, 6, 7, 8, 9}. If five integers are chosen from T, must there be two integers…

A: Concept used: The Pigeonhole principle states that if k+1 objects are to distributed in k boxes then…

Q: Which notation expresses the number of permutations of 9 items taken 6 at a​ time

A: Number of permutations of n items taken r at a time is given by Pn, r=Prn=n!n-r!

Q: Find the number of subsets of the set (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} having 4 elements. * 340…

A: Find the number of subsets of the set 1,2,3,4,5,6,7,8,9,10,11 having 4 elements

Q: Let A = {-9, -7, -6, -4, -3, 1, 3, 4, 8, 10} and B = {-7, -6, -4, 1, 4, 8, 10}. How many sets of C…

A: Given that C has a property thatfrom the second condition we can conclude that all the elements of B…

Q: Consider the set ? = {3,7,11,15,19, ... ,95,99,103}. At least how many elements must be selected…

A: In the given question we have to find the lest number of the element of the given set s.t there will…