The Mega Millions game consists of drawing five numbers from the integers 1,2,3,...,70 (without replacement). Then a special number, a sixth number, is selected from a new set of numbers 1,2,3,...,25. A winning player must have selected the correct five numbers from the first set and the correct number from the second set. You get one set of six numbers for a $2 bet. What is the probability of winning the Mega Millions game if you make a $2 bet?

2a. Two quantities a and b are said to be in the "golden ratio" when the ratio of sum of the two quantities to the larger quantity equals the ratio of the larger quantity to the smaller quantity. That is, when

where .

Define to be , that is . Show that the quadratic equation follows from the definition of golden ratio. Find the positive root of this quadratic equation and thereby find the golden ratio.