a) Compute C8,2.    b) Compute P10,6.

A monkey has filled in a 3 × 3 grid with the numbers 1, 2, . . . , 9. A cat writes down thethree numbers obtained by multiplying the numbers in each horizontal row. A dog writesdown the three numbers obtained by multiplying the numbers in each vertical column.Can the monkey fill in the grid in such a way that the cat and dog obtain the same listsof three numbers? What if the monkey writes the numbers 1, 2, . . . , 25 in a 5×5 grid? Or1, 2, . . . , 121 in a 11 × 11 grid? Can you find any conditions on n that guarantee that itis possible or any conditions that guarantee that it is impossible for the monkey to writethe numbers 1, 2, . . . , n^2 in an n × n grid so that the cat and the dog obtain the same lists of numbers? Please provide a mathematically rigorous solution with proofs that could be understood by a person at a high school level.

450 kg of dried fruit was distributed from wholesaler A (WA) and 750 kg of dried fruit was distributed from wholesaler B (WB) to bakeries X,Y and Z.  Bakery X received 157.5kg from WA and 112.5 kg from WB Bakery Y received 180 kg from WA and 450 kg from WB  Bakery Z received 112.5 kg from WA and 187.5 kg from WB.  What is the weight of dried fruit contained within the cakes sent to cake shops P & Q?

A group of 650 tourists includes 248 who have visited Germany, 115 who have visited Holland,and 319 who have visited neither Germany nor Holland. Use the Addition Principle to computehow many have visited both Germany and Holland.

A company produces three P,Q and R using raw materials A,B and C .one unit of P requires 1,2 and 3 units,of A,B and C respectively. One unit of Q requires 2,3 and 2 units of A,B and C respectively. one unit of R requires 1,2 and 2units of A,B and C respectively. The number of units available for raw materials A,B and C are 8,14 and 13 units respectively. using the matrix method, determine the number of units of each product to produce in order to utilize completely available resources

In the given grid, an ant begins at the "Start" cell and in each move, it can go either one step right or down to any adjacent cell with common side until it reaches the "End" cell. If in each move, Start 18 15 13 14 12 26 it gets the number in the square, then what is the smallest sum the ant can 17 11 19 10 get? (A) 91 (B) 95 (C) 96 8. 24 11 (D) 97 (E) 102 20 4. 19 En 10 O B 21 %3D 17 21 20 t6