Question

Suppose that three computer boards in a production run of forty are defective. A sample of five is to be selected to be checked for defects. How many different samples can be chosen, and how many samples will contain at least one defective board?

Answer 1

I know how to get the first part, but not sure what method to use for the second

Answer 2

ie there are 40C5 different samples, right

Answer 3

am I looking for the total possible combinations of 5 parts with between 1 and 3 parts defective? so, 5c1 +5c2+5c3?

Answer 4

Is this right?

Answer 5

40C5 will be the selection this is right..

Answer 6

Atleast means that there can be one defective or two or three..

Answer 7

so would it actually be 40c1 +40c2 +40c3?

Answer 8

So the combinations will be:

1 defective + 4 non defective

2 defective + 3 non defective

3 defective + 2 non defective

So combine all this..

Answer 9

oh, gotcha

Answer 10

so, 40c1*40c4+40c2*40c3+40c3*40c2?

Answer 11

So you will get:

\[\large ^{3}C_1 \times ^{37}C_4 + ^3C_2 \times ^{37}C_3 + ^3C_3 \times ^{37}C_2 \]

In my view...

Answer 12

because you're selecting from a set of 3 defective ones and 37 good ones

Answer 13

that makes sense

Answer 14

need more practice. thank you.

Answer 15

Do you have answers with you for this??

Answer 16

I don't, it's an even question in the exercises :( but I think the intuition is right.

Answer 17

So let me check now if this is right or not..

Answer 18

there were also some exercises dealing with choosing teams of mixed men and women from a large pool that were solved in a similar fashion, so I think this is right.

Answer 19

Yeah those and this are based on one concept only..

Answer 20

So congratulations we are right..

Answer 21

:) thanks for the help

Answer 22

Welcome dear...