An image depicts a hand holding a nickel, a dime, a quarter, and a fifty-cent piece. The scene transitions to a shop with a clerk who displays a variety of articles with different price tags. Each item is unique in nature and we see the prices vary so that each of them could be purchased with the coins in hand, without needing to receive change back. The items displayed range from small toys, stationery items, candy bars to small accessories. Note that the actual price tags or the question text is not visible in the image.

10. You have a nickel, a dime, a quarter and a fifty-cent piece. A clerk shows your several articles, each different price and any one of which you could purchase with your coins without receiving change. What is the largest number of articles he could have shown you?

A.8
B.10
C.13
D.15
E.21
Choice B is wrong.

1, 5c

2 10 c
3, 15 c
4, 25c
5 30C
6 35 c
7 40 c
8 50 c
9 55 c
10 60 c
11 65
12 75 c
13 80 c
14 85 c
15 90 c

Since no coin duplicates the amounts of combining other coins, the number of items could be as many as

4C1 + 4C2 + 4C3 + 4C4 = 15

Note that the sum of the nth row of Pascal's triangle is 2^n, but we are missing 4C0=1, leaving only 15 combinations.

This is also the number of elements of the power set of 4 items, excluding the empty set.

21

21

Well, it seems like the clerk needs a lesson in economics. You see, with a nickel, a dime, a quarter, and a fifty-cent piece, you have a total of 4 coins. Now let's think about it logically. The largest-priced item you could purchase without receiving change would be 50 cents, using the fifty-cent piece.

So, let's go through the possibilities. If you bought an item for 50 cents, you would be left with 3 coins. If you bought another item for 50 cents again, you would be left with 2 coins. Now, let's repeat the process: 50 cents leaves you with 1 coin, and you buy another item for 50 cents, subsequently leaving you with 0 coins.

Therefore, you can only purchase 4 items in total with these coins. So, the correct answer is definitely not B, but rather A. So, don't clown around with your choices!

To solve this problem, we need to find the largest number of articles the clerk could have shown you without receiving any change, using the given coins (nickel, dime, quarter, and fifty-cent piece).

We can start by considering the highest denomination coin, which is the fifty-cent piece. Since any article with a price of 50 cents can be purchased without receiving change, the clerk can show you one article with this price.

Next, let's consider the quarter. Any article priced at 25 cents can be purchased without receiving change when combined with the fifty-cent piece. So, the clerk can also show you one article with this price.

Now, for the combination of the fifty-cent piece and a quarter, we have already explored the possibilities with 50 cents and 25 cents. This means we can use the remaining coins (nickel and dime) to make up the remaining amount for the lowest-priced articles.

The lowest-priced article we can buy is 5 cents, using the nickel. To combine the nickel with the 50 cents and the quarter (25 cents), we would have: 50 + 25 + 5 = 80 cents.

Similarly, the dime can be combined with the 50 cents and the quarter to make up the lowest price of 10 cents. This gives us: 50 + 25 + 10 = 85 cents.

Now let's see how many 80-cent articles and 85-cent articles we can buy using the combination of the four coins.

For the 80-cent articles, we have the following options:
- We can buy 5 articles at 80 cents each (using the nickel)
- Or, we can buy 2 articles at 80 cents each (using the dime)

For the 85-cent articles, we have the following options:
- We can buy 2 articles at 85 cents each (using the nickel)
- Or, we can buy 1 article at 85 cents (using the dime)

Adding up the possibilities:
- 5 articles at 80 cents + 2 articles at 85 cents = 5 + 2 = 7 articles

From the given options, the largest number of articles the clerk could have shown you is 7, which corresponds to choice A. So, the correct answer is A.