How can the whole nunmbers from 1 to 17 be placed into the 17 disks of the diagram here so that any three numbers on the same line through the center will give the same sum?

Q: How many compositions of n are there into k parts of size at least 3?

A: How many compositions of n are there into k parts of size at least 3?

Q: Compute how many different ways there are to color the faces of a cube so that three faces are red,…

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Q: Compute the sum of the first 60 positive integers that are exactly divisible by 4.

A: The numbers divisible by 4 is:

Q: Find the number of distinct arrangements of the 9 letters in BEGINNING. Two of the same letter are…

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Q: How many five-digit numbers are there for which each digit is either equal to both adjacent ones, or…

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Q: Suppose each license plate in a certain state has four letters followed by two digits. The letters…

A: A license plate has four letter letters followed by two digits excluding I, O, Q, U and 0, 1, 2, 3.

Q: How many ways are there to fly from City 1 to City 4 with one stop?

A: Here use given table for no of ways fly from city 1 to city 4

Q: Imagine a lottery where balls numbered from 1 to 49 are placed in an urn and three are sequentially…

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Q: What is the largest number in the row starting "1 4 ..." of Pascal's triangle?   What is the sum…

A: To find what is the largest number in the row starting "1 4 ..." of Pascal's triangle? To find what…

Q: Find the number of permutations using four different numbers (2,5,11,30) if they are taken 2 at a…

A: Given that, Four different numbers are (2,5,11,30) To find: Number of permutations using four…

Q: Assume the sales representative calls 5 customers, and each call has 2 possible results: reaches the…

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Q: Show that if seven integers are selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, there must be…

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Q: Assume that you are assigning one of 12 available lockers to each of the 8 players on the team. In…

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Q: How many pairs of integers (a,b) exists such that the product of a,b and HCF of (a,b) is 1080??

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Q: A 4-sided die with numbers 1, 2, 3, 4 on the faces, is rolled n times in row, and the numbers that…

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Q: How many Lettuce paths from a to b avoiding the blue squares

A: Let us consider a 2*2 box for example. It is part of the big square.   Let say the present location…

Q: Item#3 In how many ways can 5 men and 3 women be arranged in a row if no two women are standing next…

A: Introduction: Permutation: Permutation is the method of arranging the elements. Permutation is used…

Q: Balls are numbered 1 through 10 (including 1 and 10) in an urn. 3 are drawn simultaneously and at…

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Q: Show that if any 14 numbers are selected from the set S = {1,2, 3, ..., 25}, %3D there are at least…

A: Given statement is If any 14 numbers are selected from the set S = {1,2,3,...,25}, there are at…

Q: A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a…

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Q: Compute the sum of the first 50 positive integers that are exactly divisible by 5.

A: To determine sum of the first 50 positive integers that are exactly divisible by 5.

Q: Twenty disks numbered 1 through 20 are placed face down on a table. Disks are selected one at a time…

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Q: How many combinations are there to pick r objects from 2n objects numbered from 1 to 2n with n > 2…

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Q: How many strings of 7 decimal digits are there, such that at least one of the digit is odd?

A: There are total 10 decimal digits, among which 5 are odd. Since repetition of digits is allowed,…

Q: How many pairs of two distinct integers chosen from the set {1, 2, 3, 101} have a sum that is even?

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Q: How many ways are there to distribute 7 different tasks to 7 different people if: i No roctrictions…

A: Introduction: A rule used to count the entire number of alternative outcomes in a circumstance is…

Q: n how many distinct ways can the digits in the number 1,243,520,326 be arranged? (If there are any…

A: Given number 1,243,520,326 Total number of digits=10 Number of 1's=1 Number of 2's=3 Number of 3's=2…

Q: A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a…

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Q: | Suppose 10 ducks and 6 geese line up in a single row. In how many ways can they line up so that no…

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Q: How many three digit passcode can be made from the digits 0-9in the first number is not allowed to…

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Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6, 7, 8} to guarantee that at least…

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Q: .. Five girls and three boys should be seated in line so that there are no two boys sitting next to…

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Q: Suppose we want to choose 5 objects, without replacement, from 14 distinct objects. (If necessary,…

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Q: How many different words can be formed with the letters of the word ‘SUPER’ such that the vowels…

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Q: In how many ways can 7 black and 7 white balls be distributed into 7 boxes so that there are exactly…

A: Given : 7 black and 7 white balls 7 B , 7 W Given boxes = 7  there are exactly 2 balls in each box…

Q: Each of the six squares shown in the figure is to be filled with any one of ten possible colors. How…

A: We have to tell that in how many ways six squares are shown in the figure is to be filled with any…

Q: How many polygons can be possibly made from 6 distinct points on a plane, no three of which are…

A: Answer: 42 polygons can be possibly made from 6 distinct points on a plane, no three of which are…

Q: Suppose each license plate in a certain state has one digit, followed by four letters, followed by…

A: FORMAT of number = 9AAAA9 (1 number, 4 letters, 1 number) A license plate has six spaces to be…

Q: There are twenty marbles of similar colour and size where each marble is labelled with a number from…

A: Number of marbles in total =20. Number of marbles with even number =10.  number of marbles with odd…

Q: 4. Assume that each scoop can only hold a maximum of 8 pieces. How many ways are there to sprinkle…

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Q: Ninc cards are numbered 1, 2, 2, 3, 3, 4, 6, 6, 6. n All nine cards are placed in a line, making a…

A: Topic- permutations and combinations

Q: Suppose you have 1000 blocks, each of which is 1.0 cm on a side. If all 1000 of these blocks are…

A: First consider the case of 1000 blocks stacked to give a cube 10 cm on a side. The block which have…

Q: The order of the letters in the name BERNIESANDERS are rearranged, and then each letter is either…

A: Given information: Name - BERNIESANDERS Total letters in the given word = 13Number of E's = 3 Number…

Q: A shelf displays ten vases, of which some are indistinct. Five of the vases are red, three of them…

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

Q: There are 9 periods in each working day of a school. In how many ways can one organize 5 subjects…

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Q: An 8 by 8 checkerboard has alternating black and white squares. How many distinct squares, with…

A: Given: an square box in which 64 square box (black and white)

Q: Give 5 early mathematicians and their works which they contributed in the development of the study…

A: Topic- geometry

Q: How many bit strings of length greater than equal to one and less than or equal to six are there?

A: There are 2 possible bits : 0 and 1 Bit strings of length 6 are, 2.2.2.2.2.2=26=64 Bit strings of…