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
To find the number of different arrangements Dion's grandmother can make using one of each color of small squares, we need to calculate the permutations of the small squares.
A permutation is an arrangement of objects in a specific order. In this case, we have four small squares to arrange, one each of red, green, blue, and yellow.
To calculate the number of permutations, we can use the formula for calculating permutations of n objects taken r at a time, which is given by:
P(n, r) = n! / (n - r)!
In this case, we have 4 objects (small squares) and we want to take all of them at once (r = 4).
P(4, 4) = 4! / (4 - 4)!
= 4! / 0!
= 4!
The factorial of a number is the product of all positive integers less than or equal to that number. For example, 4! (read as "4 factorial") is calculated as:
4! = 4 * 3 * 2 * 1 = 24
Therefore, Dion's grandmother can make 24 different arrangements using one each of the red, green, blue, and yellow small squares.
To show the possible arrangements, let's label the small squares as R (red), G (green), B (blue), and Y (yellow).
1. RGBY
2. RGYB
3. RBGY
4. RBYG
5. RYGB
6. RYBG
7. GRBY
8. GRYB
9. GBRY
10. GBYR
11. GYRB
12. GYBR
13. BRGY
14. BRYG
15. BGRY
16. BGYR
17. BYRG
18. BYGR
19. YRGB
20. YRBG
21. YGRB
22. YGBR
23. YBRG
24. YBGR
These are the 24 possible arrangements of the small squares that Dion's grandmother can make to create one large square block for her quilt.