19. There are ten tokens, 3 black and 7 white, are to be randomly placed into each of the unit squares of a 2x5 board, where each unit square can only fit exactly one token. How many ways are there to place the tokens such that no two black tokens are adjacent to each other? (A) 30 (B) 36 (C) 38 (D) 40 (E) 60 O A

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A: Pigeonhole principle states that if m pigeonholes are occupied by m + 1 pigeons, then at least one…

Q: If n(A ∪ B) = 60, n(A ∩ B) = 40, and n(A) = n(B),find n(A).

A: Givenn(A∪B)=60n(A∩B)=40n(A)=n(B)To find n(A)

Q: If n(A) = 12, n(A ∪ B) = 30, and n(A ∩ B) = 6, find n(B).

A:

Q: If n(A ∪ B) = 50, n(A ∩ B) = 10, and n(B) = 20,find n(A).

A: Given,n(A∪B)=50,n(A∩B)=10 and n(B)=20 To find: n(A) Solution: We know,…

Q: 11. A group of 6 boys and 5 girls shared a packet of sweets: After each of them took 3 sweets, there…

A: No.of boys in group is 6No of girls in group is 5

Q: If n(A ∪ B) = 96 and n(A) = n(B) = 67, find n(A ∩ B).

A:

Q: a 2 x 2 “corner"). Is it possible to tile the remaining squares with 3 x 1 tiles (which can be…

A: we use area of square to find the card of 3*1 is possible or not

Q: 7. Six chairs are equally spaced around a circular table. What is the number of ways that three men…

A: See this solution in below.

Q: There are 16 cubic plastic blocks, each one a different color from the others. How many ways are…

A: There are 16 cubic plastic blocks, each one a different color from the other.

Q: There is a drawer with a total of 7 socks in it. Four (4) socks are blue and three (3) socks are…

A: Four (4) socks are blue and three (3) socks are yellow

Q: Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate…

A: Given,no.of black jelly beans=5no.of red  jelly beans=1no.of yellow  jelly beans=3Total no.of  jelly…

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A:

Q: How many ways are there to have one puppy out of the four with pointy ears? 1 3. 4

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A: John has purchased 20 tiles in total, five green, 10 gold, and five white.

Q: a) In how many ways can we form a set of 5 balls from the box, 3 of them red and the remaini two of…

A: Total number of balls = 12 Number of red balls = 7 Number of green balls = 5

Q: 3. Martin wants to sell away 7 different textbooks to his friend Nathan. 2 are math textbooks, 3 are…

A: Note: Hey, since there are multiple subparts posted, we will answer first three subparts. If you…

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A: Given that the baseball manager has 12 players on his team but only nine players can play on the…

Q: If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 },C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D =…

A: Since you have asked multiple sub parts in a single request, we will be answering only the first…

Q: 6m-3k when k = 2 and m= 7

A: Given : 6m-3k

Q: 1. There are two boxes, each of which contains a certain number of cubes and balls, painted in…

A: Given:   Box 1 Box 2   Red Blue Red Blue Cube 6 24 28 42 Ball 14 56 12 18 Total 20 80 40…

Q: If n(A ∪ B) = 99 and n(A) = n(B) = 69, find n(A ∩ B).

A: Given, n(A ∪ B) = 99 and n(A) = n(B) = 69   The objective is to find  n(A ∩ B).

Q: 2. If the sum of three consecutive integers equals 60, what is the

A:

Q: 15. A rug manufacturer has decided to use five co rug, only four spindles can be used. In…

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A:

Q: Suppose there are 9 different bottles of water and 9 different bottles of juice. (i) In how many…

A:

Q: Suppose we want to choose 2 objects, without replacement, from the 3 objects pencil, eraser, and…

A: Let,P= pencil E= eraser D= deskHere we are using the formulae for permutation and combinations.

Q: How many ways can two adjacent squares be selected from an 8- by- 8checker board if we allow the…

A: first select a 2x2 square. this can be done in 7x7 = 49 ways.in each 2x2 square, one can select two…

Q: (1 2 3 4 5 6 2 3 1 5 6 4 (1 2 3 4 5 6 7 3 4 5 1 2 7 6 b. P1 = 2) and p2 = ) are the permutations on…

A: Given,  p1= 1 2 3 4 5 6 72 3 1 5 6 4 7 and  p2= 1 2 3 4 5 6 73 4 51 2 7 6 are two permutations on…

Q: If Joe only has room for 2 of his 6 flags on his flagpole, how many different ways can they be…

A:

Q: Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate…

A: Given 16 smokers 22 non smokers

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A:

Q: Tiles called tetrominoes are created from four 11 squares. The following five examples of…

A: Please note that as per our guidelines we can answer the first three sub-parts only. Please repost…

Q: How many ways are there to distribute A x Bx C blue balls to 4 people Muslum, Orhan, Ferdi, and…

A: Total number of balls = AxBxC The balls are to be distributed to 4 people. Ferdi and Bergen get no…

Q: Jack packs 3 pairs of shoes, 4 pairs of boots, 8 pairs of jeans, 9 pairs of dress pants, and 2 dress…

A: He can pick a shoe in 3 ways, a boot in 4 ways, a jeans in 8 ways, a dress pant in 9 ways, a dress…