Question

A vending machine offers 8 different drinks. One day, 6 employees each purchased a drink from the vending machine. Find the probability that at least 2 employees purchased the same drink. Round your answer to the nearest hundredth.

Answer 1

Ok tell me fist the no. of ways 6 employees can choose 8 drinks @Emilyh117

Answer 2

Each employee can get each drink @ash2326

Answer 3

Suppose I'm an employee, I have 8 choices, similarly other 5 have 8 choices. Total no. of ways 6 employees can choose to have 8 drinks
\[8\times 8\times 8\times 8\times 8\times 8=8^6\]

Do you get this?

Answer 4

Oh yeah... @ash2326

Answer 5

I get it

Answer 6

Now, we need to find the no. of ways, where at least two employees have same drink.
So the required no. of ways=
Two employees have same drink+ Three employees have same drink+four employees have same drink+5 employees have same drink+ all have same drink

Do you get this?

Answer 7

Yes @ash2326

Answer 8

is this a combination, permutation question?

Answer 9

Required no. of ways can also be found as
Total ways - (no. of ways where each have a different drink)

yeah this is a P and C problem

Answer 10

Okay. Its a permutation problem. right?

Answer 11

Both

Answer 12

What???

Answer 13

Both permutation and combination

Answer 14

How?

Answer 15

Two employees have same drink+ Three employees have same drink+four employees have same drink+5 employees have same drink+ all have same drink


We need to find the no. of ways 2 employees can be selected out of 6, that's combination

Answer 16

Okay. Would it be something like 8/6 8/5 8/5 8/3 8/2 8/1 ?

Answer 17

Easy way is to find using this
At least Two employees have same drink=Total ways - (no. of ways where each have a different drink)

Answer 18

@ash2326

Answer 19

no. of ways where each have a different drink
First person has 8 choices
second has 7
third has 6 and so on

No. of ways where each have a different drink=8*7*6*5*4*3

Answer 20

Do you get it?

Answer 21

I think so @ash2326