Please answer any of the following question and please show your work

For [ 2x^2 - 1/x]^6, determine

a) The middle term

b) The term containing x^3

Given the universal set S = {-3,-2,-1,0,1,2,3,4} and the sets A = {1,2,3,4}, B = {-3,-2,-1}, find C = {-2,-1,0,1,2}

FInd

a) A'

b) (A n C) and (B n C)

c) (B n C)'

Your are dealt one card from a standard deck of playing cards.

a) What is the probability that the card is 5?

b) What is the probability that the card is a 8 or a club?

Eight percent of the objects produced by a machine are defective. If you examine 50 objects produced by the machine, find the probability that

a) 3 are defective

b) More than 3 are defective

A class consists of 8 boys and 5 girls

a) In how many ways can a teacher choose a committee of 3 from this class?

b) How many of these committees will contain at least 1 boy?

c) How many will contain exactly 1 girl

What is the probability that number chosen from 1 to 500 is divisible by 2, 5 or 6?

A box contains 5 black balls, 4 red balls, 4 green balls, and 5 blue balls.

a) YOu select 6 balls from the box without replacing them. What is the probabilty that

you will select excatly 3 black balls?

b) You select 6 balls from the box without replacing them. What is the probability that

you draw at least 1 black balls?