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: A bag contains 12 black and 6 white balls. In how many ways can we draw from the bag groups of 5…

A:

Q: Let J = {1, 2, 3, ... }, the set of counting numbers and let R be the set of real numbers. Is R − J…

A:

Q: If a dealer randomly picks 5 cards from a standard deck that consists of 52 playing cards and then…

A:

Q: Queen chooses sixteen different numbers from the set {1, 2, 3,..., 25, 26}. Prove, or disprove, that…

A: There are total 26 numbers in the set  {1, 2, 3,..., 25, 26}. Also the queen chooses 16 different…

Q: In how many ways can four distinct numbers be chosen from the set {1,2,...,14} so that no pair among…

A: solution:- Probability when all four chosen numbers are not consecutive = 1 − Probability when all…

Q: How many different three digit numbers can be made from the set of integers {1,2,3,4,5,6,7,8,9} if…

A: The set of integers {1,2,3,4,5,6,7,8,9}

Q: Use any method, list all the three digit numbers from the set {3,4,5,6} where there are no repeating…

A:

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 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: If the first even integer is 4, then what will be next three consecutive even integers ? O 5, 14, 10…

A: In the question it is asked to represent next three consecutive even integers after even integer 4.

Q: How many different Kriyas may be created with only 5 of these poses?

A: In yoga, a Kriya is a complete set of specific poses and breathing techniques that are combined to…

Q: A collector of toy vehicles has 12 hot rod cars, 10 pickup trucks, 9 classic cars, and 1 big rig…

A:

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: A shop has 6 types of candy. How many ways are there to select 24 pieces of candy with at least two…

A: The combination principles can be used to select a number of objects from a bundle. The number of…

Q: A multiset is similar to a set, but can contain an element more than once. How many multisets can we…

A: You can identify every multiset with an ordered pair of usual sets, call them high and low. If you…

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: find all poisible tofaloğies on

A:

Q: restaurant offers a special pizza with any 4 toppings. If the restaurant has 18 topping from which…

A: restaurant offers special pizza with any 4 toppings out of 18 toppings.  no. of different special…

Q: A standard deck of cards has 52 cards. There are four suits: ♥, ♦, ♣, ♠. For each suit, there are…

A: Conditions:• The first group has three cards of the same denomination.• The second group has three…

Q: The probability of choosing an odd number in the given set of numbers 8, 13, 14, 9, 15, 11, 10 is O…

A: Given : Set of numbers : 8 , 13 , 14 , 9 , 15 , 11 , 10.

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

A: We ahave to find no. Of subsets.

Q: Let ?={1,2,3,4,5,6}. How many subsets of ?A contain an even number of elements? (How would you…

A:

Q: Let’s imagine a hand consisting of 1 card drawn from a non-standard 64-card deck with flowers on the…

A: In this problem, we are dealing with a non-standard deck of 64 cards, consisting of 4 suits with 16…

Q: Find the number of permutations of 4 distinct objects. There are permutations.

A: Permutation: Permutation is an arrangement  of items in a permanent order. In permutations  Orders…

Q: A license plate consists of   five symbols on each​ plate, where the first two symbols are letters…

A: Fundamental principle of counting : If an event occur in m ways an corresponding to it another event…

Q: An insurance agent has a list of 9 prospects and decides to telephone 5 how many different ways can…

A: THERE ARE TOTAL 9 PROSPECTS AND ON THE 1ST DAY WE NEED TO CALL THE 5 PROSPECTS THEREFORE TOTAL WAYS…

Q: Suppose that you have 7 cards. 3 are green and 4 are yellow. The 3 green cards are numbered 1, 2,…

A: Given: Number of green cards = 3            Number of Yellow cards = 4            Total number of…

Q: An Uber XL can hold between 1 and 4 people. One September evening, 5 distinct and random people need…

A: According to the given information, An uber XL can hold between 1 and 4 people. On September evening…

Q: Prizes are to be given to different people in a group of 18. In how many ways can a first prize, a…

A: Use the given information.

Q: Let S be set of integers and for any three numbers say a, b, c E N. Then, a*b* c = max{a,b,c}.…

A:

Q: There are 10 questions in a final ėxamination for Discrete Mathematics. Each question is assigned at…

A:

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

A:

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.