betsy is making a flay, she can choose three colors from red, white,blue, ang yellow. how many choices does betsey have?
assuming all colours are different ...
number of possible flags = 4 x 3 x 2 = 24
Betsy can choose three colors from red, white, blue, and yellow. To find the number of choices, we can use the combination formula. In this case, we want to find the number of combinations of colors, not the order in which the colors are chosen.
The combination formula is given by:
nCr = n! / (r! * (n-r)!)
Where n is the total number of colors available, and r is the number of colors Betsy can choose.
In this case, n = 4 (red, white, blue, and yellow) and r = 3 (Betsy can choose three colors).
Using the formula, we can calculate the number of choices Betsy has:
4C3 = 4! / (3! * (4-3)!) = 4! / (3! * 1!) = (4 * 3 * 2 * 1) / ((3 * 2 * 1) * 1) = 4
Therefore, Betsy has 4 choices when choosing three colors from red, white, blue, and yellow.
To find out how many choices Betsy has, we need to use the concept of combinations. Since Betsy can choose three colors from red, white, blue, and yellow, we need to calculate the number of combinations of 3 colors out of 4.
To calculate combinations, we use the formula:
C(n, r) = n! / (r! * (n - r)!),
where n is the total number of items and r is the number of items chosen.
In this case, n = 4 (as there are 4 colors) and r = 3 (since Betsy can choose 3 colors).
Using the formula, the calculation becomes:
C(4, 3) = 4! / (3! * (4 - 3)!)
= 4! / (3! * 1!)
= (4 * 3 * 2 * 1) / ((3 * 2 * 1) * (1))
= 24 / (6 * 1)
= 24 / 6
= 4.
Therefore, Betsy has 4 choices of color combinations for her flag.