Question

A.) How many ways can you select 1 flavor of ice cream, 1 topping and 1 drink if there are 5 flavors of ice cream, 3 toppings and 4 drinks to choose from?
B.) How many ways can you select a 4-digit passcode without repeating any digit?
C.) How many ways can you select 3 toppings for a pizza with 8 toppings to choose from?
D.) What is the probability of rolling a single die and it landing on a prime number? (Remember, the number 1 is not considered prime.)
E.) How many items are in the sample space for rolling a die and spinning a spinner with 4 different colored sections (red, yellow, green and blue)?
F.) What is the probability of rolling the die and spinning the 4-sectioned spinner described in part E, and getting the number 5 and the color red?
G.) If you wanted to purchase a size T-shirt that "most" people could wear, would you purchase the mean size, the median size or the mode size?

Answer 1

A) you can combine any of the 5 ice-creams with any of the 3 toppings and any of the 4 drinks.

This means a total of 5*3*4=60 ways.

B) assuming that the first digit can be 0, we have 10 choices for the 1. digit, 9 for the 2., 8 for the third and 7 choices for the fourth digit.

In total, there are 10*9*8*7=5040 passwords we can create.

C) Selection of 3 objects out of 8, can be done in

C(8, 3)=8!/(3!5!)=(8*7*6)/3!=8*7=56 many ways.

D.

P(prime)=n(prime)/n{1, 2, 3, 4, 5, 6}=n{2, 3, 5}/6=3/6=1/2=0.5

E.

any of the 6 outcomes of rolling a die, can be combined with any of the 4 colors.

for example (1, red), (1, yellow), (1, green), (1, blue).

so in total, there are 6*4=24 items in the sample space.

F.
(5, red) is just one of the 24 items in the sample space, so its probability is 1/24= 0.0417

G.

the mode, as it is the size which appears the most.


Answers:

A.60

B.5040

C.56

D. 0.5

E.24

F.1/24= 0.0417

G.mode