Mrs.fairweather has placed 10 tiles in a bag.one are red,some are blue,and some are yellow.how many different combination of the colors are possible?
Since it asks for "how many different combinations of the colours are possible"
we are merely interested in the number of subsets of the 4 colours.
number of subsets are 2^4 = 16
but that would include the one case of not choosing any, so
I would say there are 15 choices of colours
The answer would be the same if there were 200 tiles, as long as we have some of each of the colours
I would say their were 44 different combinations but the correct answer is 96
To determine the number of different combinations of colors possible in Mrs. Fairweather's bag, we need to consider the three colors: red, blue, and yellow. Since we know that there is 1 red tile in the bag, we have 1 option for the red tile.
Now, let's consider the blue and yellow tiles. Since Mrs. Fairweather has only stated that "some" tiles are blue and yellow, we don't have exact numbers. Therefore, we have multiple possibilities.
Let's look at a few scenarios:
- Suppose we have 1 blue tile and 8 yellow tiles. This gives us 1 blue tile option and 8 yellow tile options.
- Alternatively, let's say we have 2 blue tiles and 7 yellow tiles. In this case, we have 2 blue tile options and 7 yellow tile options.
We can continue to vary the numbers of blue and yellow tiles to find all the possible combinations.
To calculate the total number of combinations, we need to sum up the options for each color tile:
1 (option for red) * number of options for blue * number of options for yellow.
For example, if we consider the scenarios mentioned above (1 blue tile and 8 yellow tiles, and 2 blue tiles and 7 yellow tiles), the total number of combinations would be:
1 * 1 * 8 + 1 * 2 * 7 = 8 + 14 = 22.
Therefore, the number of different combinations of colors possible in Mrs. Fairweather's bag depends on the number of blue and yellow tiles she has. We need this information to determine the exact number of combinations.
To calculate the number of different color combinations that are possible with the given information, we can use the concept of combinations.
Given that there is one red tile and multiple blue and yellow tiles, let's assume the number of blue tiles is "b" and the number of yellow tiles is "y" (where b + y = 10 - 1, as the red tile is already accounted for).
We need to find the number of combinations of blue and yellow tiles. This can be calculated using the formula for combinations:
C(n, k) = n! / (k! * (n - k)!)
Where:
- n is the total number of items
- k is the number of items being chosen
In this case, n = b + y (total number of tiles) and k = 2 (choosing between blue and yellow tiles).
Since we have multiple possibilities for the number of blue and yellow tiles, we need to calculate and add up the combinations for each scenario.
For example, if we have 5 blue tiles (b = 5), then y = 4 (because b + y = 10 - 1). We can calculate the combinations as follows:
C(5 + 4, 2) = (5 + 4)! / (2! * ((5 + 4) - 2)!)
By simplifying the equation, we get:
C(9, 2) = 9! / (2! * 7!)
Now, we need to calculate the combinations for each possible value of b (from 1 to 9) and add them all up to find the total number of different color combinations.
Here is the breakdown:
For b = 1, y = 8:
C(8 + 1, 2) = (8 + 1)! / (2! * ((8 + 1) - 2)!)
For b = 2, y = 7:
C(7 + 2, 2) = (7 + 2)! / (2! * ((7 + 2) - 2)!)
For b = 3, y = 6:
C(6 + 3, 2) = (6 + 3)! / (2! * ((6 + 3) - 2)!)
...and so on, until b = 9.
Finally, we add up all the combinations calculated for each scenario (for b = 1 to b = 9) to get the total number of different color combinations possible.