Probability1

P(2 azaleas) = 2/9C2 ; P(2 Buttercup) = 3/9C2; P(2 Petunias) = 4C2/9C2

1 - P(Bouquet with identical flowers) = P(bouquet having 2 different flowers)

2/72+6/72+12/72 = 20/72

1-5/18 = 13/18

Please post the correct answer, I got a different result. Please correct me if I am wrong

2 azaleas, 3 buttercups, and 4 petunias

Probability of selecting 2 azaleas = 2/9*1/8
Probability of selecting 3 buttercups = 3/9*2/8
Probability of selecting 4 petunias = 4/9*3/8

Which gives 2/72 + 6/72 + 12/72 = 5/18

But we want probability of not having exactly same = 1 - 5/18 = 13/18

Cheers,
SVD

I guess I screwed up. 2C2 = 1

Probability at its most basic is want over total - so eventually we want to solve for

(bouquet without two same)/ All bouquets

First solve for how many bouquets can you make - with two flowers you have 9 to choose from for the first slot and 8 to choose from in the second slot but order doesn't matter so you divide by 2. Thus 9*8/2 = 36 total bouquets.

Now we need to find the nubmer of bouquets that won't have the same - there ways to look at this
Bouquet has an azalea and another flower (2 x 7)/2 = 7 bouquets
or
Bouquet has a buttercup and another flower: (3 x 6)/2 = 9 bouquets
or
Bouquet has a petunia and another flower: (4 x 5)/2 = 10 bouquets.

add up all bouquets that don't have double flowers - 26 options.

Now put you want over your total - for 26/36 = 13/18 is the final answer

Probability of choosing the same flower = 2/9 * 1/8 + 3/9 * 2/8 + 4/9 * 3/8 = 5/18


Why do we multiply with these boldenend numbers?

gunjan1208 wrote:Probability of choosing the same flower = 2/9 * 1/8 + 3/9 * 2/8 + 4/9 * 3/8 = 5/18


Why do we multiply with these boldenend numbers?

We are choosing two flower out of 9 one after the other.
So for say buttercup first flower can be chosen in 3/9 and the next buttercup flower after the fist is removed will be chosen in 2/8.

The same logic applies for the rest of the flowers.