A lottery game consists of drawing five distinct whole numbers from the numbers 1 through 62 in any order. Then one more number from the numbers 1 through 27 is selected as the final number (this number could be one of the original five). These numbers are drawn every Wednesday and Saturday. If you match all six numbers, you win the jackpot, which is worth at least $40 million. Use methods of this section to show that there are 174,717,054 possible plays. (a) The first step is to select five distinct whole numbers between 1 and 62. Order is not important. Use the appropriate counting rule to determine the number of ways groups of five different numbers can be selected.

(b) The next step is to choose the final number, which is any number between 1 and 27. The number need not be distinct from numbers chosen for the first five described in part (a). Use the appropriate counting rule to determine the number of possible distinct outcomes for the first five numbers, chosen as described in part (a) together with the final number.