Probability - By Counting

SOURCE:COMPETITION
Number of Problems: 7. : (Book)

Forty slips are placed into a hat, each bearing a number $1$ , $2$ , $3$ , $4$ , $5$ , $6$ , $7$ , $8$ , $9$ , or $10$ , with each number entered on four slips. Four slips are drawn from the hat at random and without replacement. Let $p$ be the probability that all four slips bear the same number. Let $q$ be the probability that two of the slips bear a number $a$ and the other two bear a number $b eq a$ . What is the value of $q/p$ ?

$mathrm{(A)} 162 qquad mathrm{(B)} 180 qquad mathrm{(C)} 324 qquad mathrm{(D)} 360 qquad mathrm{(E)} 720$

A set of three points is randomly chosen from the grid shown. Each three point set has the same probability of being chosen. What is the probability that the points lie on the same straight line?

$mathrm{(A) } frac{1}{21} qquad mathrm{(B) } frac{1}{14} qquad mathrm{(C) } frac{2}{21} qquad mathrm{(D) } ...$