# Mimo wishes to leave a waitress a tip. Mimo has five coins in his pocket, a penny, a nickel, a dime, a quarter, and a half-dollar. If he uses exactly three coins for the tip, how many different tips are possible?

A. 15
B. 5
C. 20
D. 10

Crystal wants to put a fence around her vegetable garden.Her garden is 5 ft wide and 4 ft long.She plans to put a post at each corner and at every foot.How many fence posts will Crystal need? (1 point)
14 posts
18 posts
19 posts
20 posts

## how many ways to combine five things three at a time?

n!/[r!(n-r)!]

5!/[3!(2!)]

5*4/2

10
==========================
4 along each long side with no ends
5 along each short side including end posts
9*2 = 18

## To solve the first problem, let's consider the number of ways Mimo can choose three coins out of the five in his pocket for the tip. We can use combinations to calculate this.

The number of ways to choose three coins out of five is given by the formula: C(5, 3) = 5! / (3! * (5-3)!) = 10.

Therefore, there are 10 different ways Mimo can choose three coins for the tip. The answer is D. 10.

Now let's move on to the second problem.

To find the number of fence posts Crystal needs, we need to add up the number of corner posts and the number of posts along the sides.

There are four corners in the garden, so Crystal needs 4 corner posts.

The length of the garden is 4 ft, so there will be 4 posts along one of the sides.

The width of the garden is 5 ft, so there will be 5 posts along the other side.

Therefore, the total number of posts required is 4 (corner posts) + 4 (posts along one side) + 5 (posts along the other side) = 13.

However, we also need to consider the additional post at the end of each foot. Since there are 4 posts along each side, there will be 4-1 = 3 additional posts along each side.

Therefore, the total number of additional posts is 3 (additional posts on one side) + 3 (additional posts on the other side) = 6.

Adding the corner posts and the additional posts, we get 13 + 6 = 19.

Therefore, Crystal will need 19 fence posts in total. The answer is C. 19.

## To find the number of different tips that Mimo can leave, we need to consider all the possible combinations of three coins.

Mimo has five coins in his pocket: a penny, a nickel, a dime, a quarter, and a half-dollar.

To calculate the number of combinations, we can use a combination formula. The formula for combinations is:

nCk = n! / (k! * (n-k)!)

where n is the total number of items or choices and k is the number of items or choices we want to select.

In this case, n is 5 (since Mimo has 5 coins) and k is 3 (since he wants to use exactly 3 coins).

Using the combination formula, we can calculate:

5C3 = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = (5 * 4 * 3!) / (3! * 2 * 1) = (5 * 4) / (2 * 1) = 10

Therefore, Mimo can leave 10 different tips using exactly three coins.

So the answer is D. 10.

Now let's move on to Crystal's question about the number of fence posts needed for her vegetable garden.

Her garden is 5 ft wide and 4 ft long. She plans to put a post at each corner and at every foot.

To calculate the number of fence posts, we need to find the total number of posts along each side and add the corner posts.

The width of the garden is 5 ft, so there will be a total of 5 + 1 = 6 posts along the width.

The length of the garden is 4 ft, so there will be a total of 4 + 1 = 5 posts along the length.

To find the total number of posts, we can add the number of posts along the width and the length, and then subtract the 4 corner posts (as they were counted twice):

Total number of posts = (number of posts along the width + number of posts along the length) - 4

Total number of posts = (6 + 5) - 4 = 11 - 4 = 7

Therefore, Crystal will need a total of 7 fence posts for her vegetable garden.

So the answer is not provided in the given options.