How many different ways could you choose three pants to pack for a weekend trip, if you have 12 pants to choose from? Assume the pants are selected without replacement.

a. 12! / 3!
b. 12! / 9!
c. 12! / 8!⋅4!
c. 12! / 9!⋅3!

If the expected value of an extended warranty sold by an electronics store is $21, what does that mean?
a. by the customer.
b. The store makes $21 in revenue each time they sell this warranty.
c. If store sells this same warranty many, many times, they will make (on average) $21 in revenue for each warranty sold.
d. If a customer purchases this warranty and their item breaks, the store will lose $21 when they replace the item.

The key word is "choose" so the order does not matter

you are choosing 3 of 12 which is
C(12,3) = by definition 12!/(3!9!)

btw, those brackets are necessary when typing it like that
the correct choice of c) should have those brackets

Can you explain the second question? I believe it might be b or c

a. The expected value of an extended warranty sold by an electronics store is $21, what does that mean?

c. If the store sells this same warranty many, many times, they will make (on average) $21 in revenue for each warranty sold.

For the first question, the task is to calculate the number of different combinations of three pants that can be chosen from a set of 12 pants. Since the pants are selected without replacement, each selection reduces the number of available pants.

The answer to this question is option c.

We can calculate the number of combinations using the formula for combinations without replacement, which is:

nCr = n! / (r!(n-r)!)

Where n is the total number of items in the set (12 in this case) and r is the number of items to be selected (3 in this case).

So, applying the formula:

12C3 = 12! / (3!(12-3)!)
= 12! / (3!9!)

Simplifying further:

12! / (3!9!) = 12! / (8!4!)

Hence, the answer is option c.

For the second question, when it says the expected value of an extended warranty sold by an electronics store is $21, it means that if the store sells this warranty many, many times, they will make (on average) $21 in revenue for each warranty sold.

So the answer is option c.

The expected value is a calculation used in probability theory and statistics to represent the average outcome of a random variable. In this case, it represents the average amount of revenue the store can expect to make from selling the warranty.