Combinatorics | Number Theory Answers

Venn Diagram Question:
A group of 40 students were asked which sports they play in school. 18 said they play rugby. 5 said they play soccer and basketball. 5 said they play soccer and rugby but not basketball. 7 said they play rugby only. 2 said they play all three sports. Using x to represent the number of students who play rugby and basketball but not soccer solve for x.
Twice as many students play basketball only as play soccer only. Find the minimum number of students who play neither of these sports. Find the maximum number of students who play neither of these sports.

Red – 27,25,12,19,18,21,16,23,14,9,30,7,32,5,34,3,36,1
Black – 10,29,8,31,6,33,4,35,2,28,26,11,20,17,22,15,24,13
Green – 00,0
Even – 2B,4B,6B,8B,10B,12R,14R,16R,18R,20B,22B,24B,26B,28B,30R,32R,34R,36R
Odd – 1R,3R,5R,7R,9R,11R,13B,15B,17B,19R,21R,23R,25R,27R,29B,31B,33B,35B
From these, determine each of the following:

A∪B
A∩D
B∩C
C∪E
B∩F
E∩F

Find the total number of combinations of 4 digits that can be obtained by selecting from 1,2, 4, 4, and 5. The answer from the is 4 but I need to find the steps leading to it. Thank you.

Find the G.C.F. and L.C.M. of the following sets of polynomials:
a) x^2-3xy+2y^2 and 4x^2-16xy+16y^2
b)y^2-16, y^2-4 and y^2-3y+2
Simplify:
a)9x^2+81x / x^3+8x^2-9x
b)1/x^2 -4 / 1/x -2