Consider a 48-ball lottery game. In total there are 48 ballsnumbered 1 through to 48 inclusive. Seven balls are drawn (chosenrandomly), one at a time, without replacement (so that a ball cannotbe chosen more than once). To win the grand prize, a lottery playermust have the same numbers selected as those that are drawn. The orderof the numbers is not important so that if a lottery player haschosen the combination 1, 2, 3, 4, 5, 6, 7 and, in order, thenumbers 4, 3, 5, 1, 2, 7, 6 are drawn, then the lottery playerwill win the grand prize (to be shared with other grand prizewinners). You can assume that each ball has exactly the same chance of being drawn as each of the others.

(a)Consider the 48-ball lottery game described above. In how many different ways can you select a sample of seven balls from a population of 48 balls?

1) 609839876

2) 7

3) 876029087

4) 41

5) 73629072

(b)Consider the 48-ball lottery game described above. Recall that the order of the numbers chosen is not important and that each number can only be chosen once. In total, how many combinations are there available that include the numbers 1, 2, 3, 4 and 5but NOT the numbers 6 or 7?

1) 7

2) 820

3) 903

4) 902

5) 48