Question

a bag of gumballs contain 4 grape flavored balls, 5 cherry flavored balls, and 6 lemon flavored balls. determine the probability of seecting 2 grape balls, 4 cherry balls and 4 lemon balls?

Answer 1

Answer)

Here we have 4 grape balls + 5 cherry balls + 6 lemon balls

Total = 4 + 5 + 6 = 15

We need to select 2 grape balls, 4 cherry balls and 4 lemon balls

That is 2+4+4 = 10

We can select r out of n items in ncr ways

Where,

Ncr = n!/(r!*(n-r)!)

Where n! = n*n-1*n-2*n-3*n-4*n-5*....till 1

For example

5! = 5*4! = 5*4*3! = 5*4*3*2! = 5*4*3*2*1

So, 15c10 = 3003

Total = 3003

Favorable = 2 grape balls, 4 cherry balls and 4 lemon balls

= 4c2*5c4*6c4

= 6*5*15

= 450

Probability = 450/3003 = 0.14985014985