MathDB
Ratio of Probabilities of Slips Placed in a Hat

Source:

January 14, 2009
ratioprobability

Problem Statement

Forty slips are placed into a hat, each bearing a number 1 1, 2 2, 3 3, 4 4, 5 5, 6 6, 7 7, 8 8, 9 9, or 10 10, with each number entered on four slips. Four slips are drawn from the hat at random and without replacement. Let p p be the probability that all four slips bear the same number. Let q q be the probability that two of the slips bear a number a a and the other two bear a number b\not\equal{} a. What is the value of q/p q/p? <spanclass=latexbold>(A)</span> 162<spanclass=latexbold>(B)</span> 180<spanclass=latexbold>(C)</span> 324<spanclass=latexbold>(D)</span> 360<spanclass=latexbold>(E)</span> 720 <span class='latex-bold'>(A)</span>\ 162\qquad <span class='latex-bold'>(B)</span>\ 180\qquad <span class='latex-bold'>(C)</span>\ 324\qquad <span class='latex-bold'>(D)</span>\ 360\qquad <span class='latex-bold'>(E)</span>\ 720