A pack of Jellybeans contains 7 different flavors: Apricot, Banana, Coconut, Date, Eggplant, Fig, and Grape. You can Eat each flavor individually or come up with some crazy combinations. How many flavor combinations are possible with these 7 flavors alone or mixed? You can use only use one flavor per combination. Example, no ABBC, but ABDEF is good.
7+7*6+ 7*6*5 + 7*6*5*4+7*6*5*4*3+ 7*6*5*4*3*2+ 7*6*5*4*3*2*1
you can eat in combinations of 1,2, ...6,7
So how many many flavor combinations
do the math. Add them up.
To find the total number of flavor combinations possible with these 7 flavors, you can use the concept of combinations without repetition. Since you can only use one flavor per combination and the order of flavors does not matter, you can use the formula for combinations without repetition, which is n choose r.
In this case, you have 7 flavors to choose from, and you can choose any number of flavors from 1 to 7.
To get the total number of combinations, you need to sum up all possible combinations for each number of flavors chosen.
Number of combinations with 1 flavor:
Since you can choose any one flavor from the 7 available, there are 7 combinations possible when you choose only one flavor.
Number of combinations with 2 flavors:
To find the number of combinations with 2 flavors, you can use the formula 7 choose 2.
7 choose 2 = 7! / (2!(7-2)!) = (7 * 6) / (2 * 1) = 21 combinations.
Number of combinations with 3 flavors:
Using the formula 7 choose 3, you can calculate:
7 choose 3 = 7! / (3!(7-3)!) = (7 * 6 * 5) / (3 * 2 * 1) = 35 combinations.
By applying this pattern for all possible numbers of flavors chosen, we can find the total number of flavor combinations:
Total combinations = 1 (1 flavor) + 21 (2 flavors) + 35 (3 flavors) + 35 (4 flavors) + 21 (5 flavors) + 7 (6 flavors) + 1 (7 flavors) = 121 combinations.
Therefore, there are 121 flavor combinations possible with these 7 flavors alone or mixed.