Practice Exam Questions Flashcards
In how many ways they can order 30 different books on one shelf. Pick the correct answer from the following options:
30!
The second quiz task is all about variations without replacement.
In swimming, there is an event called a medley relay in which 4 male competitors each swim 1 of the 4 strokes. The order is as follows:
Competitor 1: Backstroke
Competitor 2: Breaststroke
Competitor 3: Butterfly
Competitor 4: Freestyle
The coach decides who swims each stroke. Suppose the team has 3 competitors who swim backstroke, 4 swimming breaststroke, 2 for the butterfly style, and 5 freestylers. How many different options are there for this team, in accordance with the medley relay rules?
120
We use variations without repetition here because the order of each relay matters; there cannot be a single competitor swimming twice in the relay either. We have 3 backstrokers, therefore, 3 options for the first position. Similarly, we have 4 breaststrokers, so 4 options for the second position. There are 2 swimmers for the butterfly position, meaning 2 options.
Finally, as there are 5 freestylers, we have 5 options for the last position in the relay.
Overall, we have the following formula obtaining the result:
ピメど＊レトレーぽ」★ぼ」12ーッパッー3+4*2+5=120
The next quiz question involves a lottery. The rules of this specific lottery game are the following:
A player chooses 6 out of 49 numbers with each ticket. The player then wins the jackpot of $500,000 if they guess all 6 of the numbers, such that their order doesn’t matter. However, there is a prize for guessing 5 out of 6 numbers which is $1,000. What is the probability of winning the $1,000 prize with a single ticket?
You go into an ice cream shop where they have the flavors vanilla, chocolate, mango, banana, and pineapple available. Going into the shop, your intentions are to get two scoops of ice cream. How many possible combinations of flavors can you have if you also allow the two scoops to be the same flavor?
John goes to the same ice-cream shop, which offers the flavors vanilla, chocolate, mango, banana, and pineapple. This time, however, the staff servers the ice cream in special cups with 2 distinct places for ice cream - Taste 1 and Taste 2, respectively.
John decides to follow the suggested order so he’ll try the ice cream in Taste 1 first. However, John also doesn’t like starting with fruit-flavored ice cream. Bearing in mind that the flavors in both Taste 1 and Taste 2 can be the same, what is the probability of John getting a desirable ice cream flavor amongst all variations?
