dion's grandmother is making a quilt using four small squares put together to form one large large square block. how many different can she make using one each of red, green, blue, and yellow smalle squares? show the possible arrangements
The answer is 24.
One way to solve:
For each color, there are 6 possible ways Deon's Grandma can arrange the smaller squares:
1. R G B Y
2. R G Y B
3. R B G Y
4. R B Y G
5. R Y B G
6. R Y G B
So 4 x 6 = 24.
Another way to solve is to use permutations: 4P4 = 4! = 4 x 3 x 2 x 1 = 24
To find the number of different arrangements, we need to consider the total number of possible permutations of the four small squares.
Since we have four squares (red, green, blue, and yellow), we can use the formula for permutations to calculate the possible arrangements:
P(n) = n!
In this case, n = 4, so we have:
P(4) = 4!
To calculate 4!, we multiply all whole numbers from 1 to 4:
4! = 4 x 3 x 2 x 1 = 24
So there are 24 different arrangements that Dion's grandmother can make using one each of the red, green, blue, and yellow small squares.
Now let's list the possible arrangements:
1. Red, Green, Blue, Yellow
2. Red, Green, Yellow, Blue
3. Red, Blue, Green, Yellow
4. Red, Blue, Yellow, Green
5. Red, Yellow, Green, Blue
6. Red, Yellow, Blue, Green
7. Green, Red, Blue, Yellow
8. Green, Red, Yellow, Blue
9. Green, Blue, Red, Yellow
10. Green, Blue, Yellow, Red
11. Green, Yellow, Red, Blue
12. Green, Yellow, Blue, Red
13. Blue, Red, Green, Yellow
14. Blue, Red, Yellow, Green
15. Blue, Green, Red, Yellow
16. Blue, Green, Yellow, Red
17. Blue, Yellow, Red, Green
18. Blue, Yellow, Green, Red
19. Yellow, Red, Green, Blue
20. Yellow, Red, Blue, Green
21. Yellow, Green, Red, Blue
22. Yellow, Green, Blue, Red
23. Yellow, Blue, Red, Green
24. Yellow, Blue, Green, Red
These are the 24 possible arrangements.