A caterer offers a choice of five desserts from a list of eight for the dessert bar at the prom. How many different groups of desserts could be served?
please check my answer = 120
8choose5 = 56, not 120
can you tell me how you got that please
Your are choosing 5 from 8 items
This is defined as C(8,5) , called "8choose5" and
calculated at 8!/(5!3!)
To find the number of different groups of desserts that could be served, we need to use the concept of combinations. In this case, we are selecting a group of 5 desserts from a total of 8 options.
The formula for combinations is given by nCr, where n represents the total number of options available and r represents the number of options we want to select:
nCr = n! / (r! * (n-r)!)
In this case, we want to find the number of combinations when selecting 5 desserts from a total of 8, so we have:
8C5 = 8! / (5! * (8-5)!)
Now let's calculate it step by step:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
5! = 5 * 4 * 3 * 2 * 1 = 120
(8-5)! = 3! = 3 * 2 * 1 = 6
Plugging these values back into the formula:
8C5 = 40,320 / (120 * 6)
= 40,320 / 720
= 56
So, the correct answer is 56, not 120. There are 56 different groups of desserts that could be served at the prom.