A quilter has 15 different squares made up, 8 with blue as the main colour, 4 with gold, and 3 with green. What
is the total number of ways the quilter can choose 2 squares of each colour for a table runner?
8C2 * 4C2 * 3C2
Well, it seems like the quilter wants to create a colorful table runner! Let's break it down, shall we?
To choose 2 squares of each color, we can start by selecting 2 out of 8 blue squares. This can be calculated as "8 choose 2" or C(8, 2), which equals 28.
Next, for the gold squares, we have 4 of them, and we want to choose 2 out of the 4. So, "4 choose 2" or C(4, 2) equals 6.
Finally, for the green squares, we have 3 of them, and we also want to choose 2 out of the 3. So again, "3 choose 2" or C(3, 2) equals 3.
To find the total number of ways, we multiply these three combinations together: 28 * 6 * 3 = 504.
Therefore, the quilter has a grand total of 504 different ways to choose 2 squares of each color for the table runner. That's a lot of possibilities for a colorful creation!
To find the total number of ways the quilter can choose 2 squares of each color, we can use combination formula.
First, let's calculate the number of ways to choose 2 squares from each color:
For the squares with blue as the main color:
Number of ways to choose 2 squares from 8 blue squares = C(8,2)
For the squares with gold as the main color:
Number of ways to choose 2 squares from 4 gold squares = C(4,2)
For the squares with green as the main color:
Number of ways to choose 2 squares from 3 green squares = C(3,2)
Now, let's calculate each combination:
C(8,2) = 8! / (2! * (8-2)!) = 28
C(4,2) = 4! / (2! * (4-2)!) = 6
C(3,2) = 3! / (2! * (3-2)!) = 3
Next, let's calculate the total number of ways the quilter can choose 2 squares of each color:
Total number of ways = C(8,2) * C(4,2) * C(3,2)
Total number of ways = 28 * 6 * 3
Total number of ways = 504
Therefore, the quilter can choose 2 squares of each color in 504 different ways for a table runner.
To find the total number of ways the quilter can choose 2 squares of each color, we can use the concept of combinations.
First, let's calculate the number of ways to choose 2 squares out of 8 blue squares. We can use the formula for combinations, which is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of items and r is the number of items we want to choose. In this case, n = 8 (the number of blue squares) and r = 2 (we want to choose 2 squares).
Using the formula, the number of ways to choose 2 blue squares is:
C(8, 2) = 8! / (2! * (8 - 2)!) = 8! / (2! * 6!) = 28
Now, let's calculate the number of ways to choose 2 squares out of 4 gold squares:
C(4, 2) = 4! / (2! * (4 - 2)!) = 4! / (2! * 2!) = 6
Finally, let's calculate the number of ways to choose 2 squares out of 3 green squares:
C(3, 2) = 3! / (2! * (3 - 2)!) = 3! / (2! * 1!) = 3
Since we want to choose 2 squares of each color, we need to multiply the number of ways to choose squares of each color together:
Total number of ways = Number of ways to choose blue squares * Number of ways to choose gold squares * Number of ways to choose green squares
Total number of ways = 28 * 6 * 3 = 504
Therefore, the quilter can choose 2 squares of each color for the table runner in a total of 504 ways.