Teo has a combination of quarters loonies and toonies in his pocket .He knows he has 9 coins in total and that he has atleastone of each type of coin.

Question

a) what is the probability that teo has more than $8
b) How many different combinations of coins could teo useto pay for an item that costs between $10 and $12, if he uses fewer toonies than loonies

Answer 1

a) There are only a few possible coin combinations that Teo could have:

1 quarter, 4 loonies, 4 toonies
2 quarters, 3 loonies, 4 toonies
3 quarters, 2 loonies, 4 toonies
4 quarters, 1 loonie, 4 toonies

In order for Teo to have more than $8, he must have at least 3 toonies. Looking at the possible combinations above, only the first one has 3 or more toonies. Therefore, there is only one possible combination of coins that satisfies this condition.

The probability of Teo having this particular combination is:

P = (number of ways to get this combination) / (total number of possible combinations)
P = 1 / (4 choose 1 * 4 choose 1 * 1 choose 1) (since there is only one way to get this particular combination)
P = 1/16

b) To find the number of different combinations Teo could use to pay for an item between $10 and $12, we need to consider the possible numbers of quarters, loonies, and toonies he could use.

- If he uses 0 quarters, he needs to use 10 loonies and/or toonies. He can use any combination of 10 coins (since he has at least one of each type), so there are 10 choose 10 = 1 possible combination.
- If he uses 1 quarter, he needs to use 9 loonies and/or toonies. He can use any combination of 9 coins (since he has at least one of each type), so there are 9 choose 1 = 9 possible combinations.
- If he uses 2 quarters, he needs to use 8 loonies and/or toonies. He can use any combination of 8 coins (since he has at least one of each type), so there are 8 choose 2 = 28 possible combinations.
- If he uses 3 quarters, he needs to use 7 loonies and/or toonies. He can use any combination of 7 coins (since he has at least one of each type), so there are 7 choose 3 = 35 possible combinations.

Therefore, there are a total of 1 + 9 + 28 + 35 = 73 different combinations of coins that Teo can use to pay for an item between $10 and $12, if he uses fewer toonies than loonies.