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?

Question

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

Answer 1

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

Answer 2

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.

Answer 3

21

Answer 4

21