Question

1) A local cafe is offering free samples for ten different coffee flavors. After sampling, the customer must rank the flavors in order of preference. What are the chances that you guess the 4 least liked flavors correctly and in the correct order?

2) Find the equation of the line through (2,0) which is perpendicular to the line: y=2/3x+7

3) A coffee shop offers 18 different types of flavor shots. If a customer can choose any number of flavor shots to have in their coffee, how many flavor shot combinations are possible?

Please answer all three questions!! I need help for my math final.

Answer 1

1) Total 10 flavors are there, and we need to find 4 with correct order. Hence, we use permutation.

Total ways = P(10, 4) =

Hence, total 5040 ways are there to select and order 4 out of 10.

There is only 1 way when we get 4 least liked flavor in correct order.

P = 1/5040

Hence probability is 1/5040

2) slope of the given line = 2/3

slope of perpendicular line =

Point is (2, 0)

This is the equation of line.

3) For each flavor we have 2 ways take it or don't take it.

So, total ways = 2^(18) = 262144

So, there are total 262144 flavor shots combination possible.

I hope these will help. Thank you.