After the last game of the season a football team goes out for ice cream. Each player orders a triple cup of ice cream with a topping.Each order has 3 diffrent flavors, order doesnt matter.The shop has 7 diffrent flavors and 2 toppings to choose from iss it possible for each member of the team to have a diffrent order of an ice cream, where order doesnt matter, with one toppingif order of the flavors deont matter? help!!
How many players are on this team?
Doesnt give it.
Then you don't have enough information to solve this problem.
Hmmm, doesnt give number of players, its a question from the instructor, can anyone figure this out? its a probabilities question, not even sure how to approach it, anyone?
Ask the instructor about the number of players on the team.
To determine whether it is possible for each member of the team to have a different order of ice cream with one topping, we need to consider the total number of unique orders and compare it to the number of players on the team.
Here's how we can calculate it step by step:
Step 1: Calculate the total number of unique ice cream orders without considering the toppings.
Since each cup has 3 different flavors and the order of flavors doesn't matter, we need to calculate the number of combinations.
Using the combination formula "nCr" (n Choose r), where n is the total number of flavors and r is the number of flavors in each cup, we have:
nCr = n! / (r!(n-r)!)
In this case, we have 7 flavors to choose from and each cup has 3 flavors.
So, 7C3 = 7! / (3!(7-3)!) = 7! / (3!4!) = (7 * 6 * 5) / (3 * 2 * 1) = 35 unique ice cream combinations (without toppings).
Step 2: Calculate the total number of unique orders with one topping.
For each unique ice cream order, there are 2 possible toppings to choose from.
So, by multiplying the number of unique ice cream orders by the number of possible toppings, we get:
35 * 2 = 70 unique ice cream orders with one topping.
Step 3: Check if the total number of unique ice cream orders with one topping is greater than or equal to the number of players on the team.
If the number of unique ice cream orders with one topping is greater than or equal to the number of players (which you haven't mentioned), then it is possible for each member of the team to have a different ice cream order with one topping.
For example, if there are 11 players on the team, and we have 70 unique ice cream orders with one topping, which is greater than 11, then it is possible for each player to have a different order.
However, if the number of unique ice cream orders with one topping is less than the number of players, then it is not possible for each member of the team to have a different order.
Please provide the number of players on the team to determine whether it is possible for each player to have a different order with one topping.