I have 2 coins, how much money might I have?
How many different amounts might I have?
List the possible combinations of
1, 5, 10, 25, 50 and 100 cent coins, in pairs, with the order unimportant. (A penny and a nickel is the same as a nickel and a penny, for example).
I get the number of possibilities to be 6+5+4+3+2+1= 7*6/2 = 21
To determine how much money you might have with 2 coins, you can consider the different combinations of coins.
Let's assume you have coins of denominations 1, 5, 10, 25, 50, and 100 cents.
To create pairs of coins, you can use a combination formula. In this case, you want to choose 2 coins from a set of 6 denominations. The order of the coins doesn't matter, so it's a combination rather than a permutation.
The formula to calculate combinations is:
C(n, r) = n! / (r!(n - r)!)
Where n is the total number of items and r is the number of items you want to choose.
For our case, let's calculate the number of combinations of 2 coins from the set of 6 denominations:
C(6, 2) = 6! / (2!(6 - 2)!) = 6! / (2!4!) = (6 * 5 * 4!) / (2 * 1 * 4!) = (6 * 5) / (2 * 1) = 30 / 2 = 15
So, there are 15 different combinations of 2 coins from the given set.
Now, to calculate the amount of money for each combination, we can list them:
1 + 5 = 6 cents
1 + 10 = 11 cents
1 + 25 = 26 cents
1 + 50 = 51 cents
1 + 100 = 101 cents
5 + 10 = 15 cents
5 + 25 = 30 cents
5 + 50 = 55 cents
5 + 100 = 105 cents
10 + 25 = 35 cents
10 + 50 = 60 cents
10 + 100 = 110 cents
25 + 50 = 75 cents
25 + 100 = 125 cents
50 + 100 = 150 cents
Therefore, you can have any of these 15 different amounts of money with 2 coins, depending on the combinations you choose.