If no letters are to be repeated and the letters Z and N are not used, then there are  possible 3-letter combinations. If no digits are to be repeated, then there are  possible 3-digit combinations. Multiply these two results together, and you get a total of 8,743,680 possible license plates .

When determining the probability of independent events, you multiply the probability of each event occurring. 

The probability of a single girl choosing a specific movie is 1 out of 6, so to find the probability of this happening the same 3 times, you multiply 1/6 three times:

When determining the probability of several events occuring independently, you use the multiplication rule, meaning that you multiply the probability of each individual event occuring. 

In this problem, the events are independent, meaning that each person's soda order does not affect the probabilty of someone else's order.

The probability of one person choosing Soda1 is 1 out of 2, or .

The probability of all five people ordering Soda1 is:

When determining the probability of several events occuring independently, you use the multiplication rule, meaning that you multiply the probability of each individual event occuring. 

In this problem, the events are independent, meaning that each person's number choice doesn't impact the other person's number choice

The probability of one person choosing a specific number is .

The probability of all 3 people choosing the same specific number is:

In a single roll of a dice, rolling a 4 is mutually exclsuve of getting a 2. Therefore we will use the addition rule to find the probability of getting a 2 or a 4.

First, find the probability of each seperate event.

Because the problem asks for the probability of a 2 "or" a 4, we will add the probability of each event.

If the school starts with  tutors, it can expect  to still be tutoring at the end of the first year. After that, we expect only  percent or  tutors to leave. So at the end of the second year, there will be the  original tutors hired the at the start of the first year and the  remaining tutors who were hired at the start of the second year. .

You must use the multiplication rule which is the probability of one event happening after one has already taken place is the product of both probabilities.  The probability of drawing a non-spade on the first draw is .  Since there is no replacment, there are now 51 cards in the deck.  The probability of drawing the spade on the second draw is .  The probability of both happening after one another is then  = 

There are 2 ways Karen gets 5 chips of the same color: she gets all 5 greens, or 5 blues. there is only 1 way to get all 5 greens: probability of which can be calculated as;

to calculate p(allblue) we use:

since order doesn't matter and chips are being drawn without replacement, this is an acceptable calculation and summing them yields 

Total likelihood of making the shot = sum of likelihood of making 1st shot+2nd shot+...

1st shot=

2nd shot=.

3rd shot=

4th=

5th=

6th=

This is multiplication rule. let's calculate the chance frank doesn't fall.

For the first jump this is , the first two is , first 3: , first 4:, first 5:, first 6:, first 7:.

Since the 7th jump drops his survival rate below % (his fall rate above 60%) we would caution Frank to stop after his 6th jump, even if the 7th jump isn't that far