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.
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
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.
a) To find the probability that Teo has more than $8, we need to determine the number of possible combinations of coins that meet this condition and divide it by the total number of possible combinations.
Since Teo has 9 coins in total, the possibilities for the number of quarters, loonies, and toonies are:
Quarters: 1-7
Loonies: 1-8 (we deduct one as he has at least one quarter)
Toonies: 1 or 2 (we deduct one as he has at least one quarter)
Now, let's calculate the number of combinations that meet the condition of having more than $8.
1 quarter + 7 loonies + 1 toonie = $8.25
1 quarter + 6 loonies + 2 toonies = $8.50
1 quarter + 5 loonies + 2 toonies = $8.75
1 quarter + 5 loonies + 1 toonie = $8.25
1 quarter + 4 loonies + 2 toonies = $9.00
There are 5 combinations in total that meet the condition.
The total number of possible combinations is:
7 possible choices for quarters * 8 possible choices for loonies * 2 possible choices for toonies = 112
Therefore, the probability that Teo has more than $8 is:
5 combinations / 112 total combinations = 5/112 ≈ 0.0446 or 4.46%.
b) To find the number of different combinations of coins Teo can use to pay for an item between $10 and $12 while using fewer toonies than loonies, we need to consider the possibilities for the number of quarters, loonies, and toonies.
The possibilities for the number of coins are as follows:
Quarters: 1-7
Loonies: 2-8
Toonies: 1 or 2 (fewer than loonies)
We need to sum up the possible combinations of coins for each range of the number of coins:
For an item costing $10:
2 quarters + 2 loonies + 1 toonie = 11 coins
1 quarter + 3 loonies + 1 toonie = 10 coins
For an item costing $11:
2 quarters + 3 loonies + 1 toonie = 12 coins
1 quarter + 4 loonies + 1 toonie = 11 coins
3 quarters + 2 loonies + 1 toonie = 12 coins
For an item costing $12:
2 quarters + 4 loonies + 1 toonie = 13 coins
1 quarter + 5 loonies + 1 toonie = 12 coins
3 quarters + 3 loonies + 1 toonie = 13 coins
2 quarters + 3 loonies + 2 toonies = 12 coins
Therefore, there are a total of 9 different combinations of coins that Teo can use to pay for an item between $10 and $12, while using fewer toonies than loonies.