Counting Problem (ways of choosing 3 with conditions)

[mishima]

Homework Statement

Given 9 good light bulbs and 4 defective light bulbs, how many ways can you select 3 such that you get exactly 1 defective bulb?

Homework Equations

C(n,r)

The Attempt at a Solution

I understand total ways to select is C(13,3)=286, and that total ways to select only good bulbs is C(9,3)=84. Subtracting these would give 202 ways to get 1 or more defective bulb. Not sure how to further differentiate these cases...answer provided is 144.

If I just use rule of counting, I can pick from 4 bad, 9 good, then 8 bad in any order which is 288...double the provided answer.

 

[Samy_A]

Homework Statement

Given 9 good light bulbs and 4 defective light bulbs, how many ways can you select 3 such that you get exactly 1 defective bulb?

Homework Equations

C(n,r)

The Attempt at a Solution

I understand total ways to select is C(13,3)=286, and that total ways to select only good bulbs is C(9,3)=84. Subtracting these would give 202 ways to get 1 or more defective bulb. Not sure how to further differentiate these cases...answer provided is 144.

If I just use rule of counting, I can pick from 4 bad, 9 good, then 8 bad in any order which is 288...double the provided answer.

In how many ways can you select 1 defective bulb?
In how many ways can you select 2 good bulbs?

 

[mishima]

C(4,1)*C(9,2). Thank you.