In the Wacko Lottery, players pay $5.00 and get to pick six numbers ranging from

Question

In the Wacko Lottery, players pay $5.00 and get to pick six numbers ranging from 0 to 60.

a) Does it matter whether or not you can pick the same number more than once? Why or why not?

b) Does order matter here? Why or why not?

c) Assuming that the same number can be picked more than once, how many possible pick-six lottery numbers are there?

d) Assuming that the order matters and the same number cannot be picked more than once, how many possible pick-six lottery numbers are there?

e) If the order doesn't matter and the same number cannot be picked mroe than once, how many possible pick-six lottery numbers are there?

f) What is the probability of any one particular lottery number - say 12 23 10 09 45 60 - coming up if order doesn't matter and the same number cannot be picked more than once?

Explanation / Answer

(A)

If the same number is picked more than once, probability of winning decreases because selection of same number decreases the options available. Hence selection of same number matters i.e. it affects the winning chances.

(B)

Order does not matter, because there only one winning number in each draw.

(C)

If the same number can be picked more than once selection of 6 numbers from 0 to 60 can be done in (61C1)^6 = 61^6

(D)

In this case as same number can not be picked more than once, number of possible ways are 61C6

But order of number matters, hence possible ways are 61C6 * 6!

(E)

In this case possible ways are 61C6

(F)

probability that one particular lottery number coming up is 6/61 = 0.0984

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