Permutation and Combination

[nikgul6218]

There are 5 blue balls, 3 red balls and 4 green balls. One has to select 4 balls from this set. In how many ways can this be done ?

a. 125
b. 495
c. 60
d. 120
e. 490

In such questions do we have to assume that the balls given are not identical ?

And will it be mentioned in the exam whether the balls are identical or not identical ?

PS- I know a silly question to ask, but please help ..

[tommywallach]

Hey Nik,

All the red balls are identical, all the blue balls are identical, and all the green balls are identical. There would be no reason to have colors in the first place if each ball were unique. In that case, they could just say nine balls. So no, real questions will look the same as this one, because it's clear from the asking how it would have to work. I think you're overthinking it (worrying they're trying to trick you or something).

-t

[nikgul6218]

Hey tommy

I think I could not articulate my thoughts well with this question.

Let us say we have 2 red balls, 1 green ball, and 1 blue ball. Now we have to select 2 balls from this set.

Your logic-
You assume that 2 red balls are identical in nature. Now in such situation there would be only 4 combinations possible.
1.both balls are red
2.1 is red other one is blue
3.1 is red other one is green
4.1 in green other one is blue

Now my doubt is, if it is not mentioned in the question that whether these red balls are identical or not then this case is also possible :

Let R(1), R(2), G, B be 4 balls, where R(1) and R(2) are not identical. So now if we have to select 2 balls from this set 6 possibilities would be there

1. R(1) and R(2)
2.R(1) and G
3. R(1) and B
4.R(2) and G (This case would be identical to [R(1) and G] if we consider that both R(1) and R(2) are identical)
5. R(2) and B( Similarly this)
6.G and B


I hope it is more clear now !

Please Help

Thanks

[tommywallach]

As I said, they are always considered identical and interchangeable.

-t

[nikgul6218]

Thank you tommy !

P.S. - Would you mind answering this ?

There are 5 blue balls, 3 red balls and 4 green balls. One has to select 4 balls from this set. In how many ways can this be done ?

[tommywallach]

There are 5 blue balls, 3 red balls and 4 green balls. One has to select 4 balls from this set. In how many ways can this be done?

I would just count them. But because order doesn't matter, the numbers will be small. Start with something simple, all the ways that you could pick 4 balls that have greens involved:

GGGG
GGGR
GGGB
GGBR
GGRR
GGBB
GRRR
GRRB
GRBB
GBBB

That's 10. Now let's count all the ways to pick 4 with NO greens:

RRRB
RRBB
RBBB
BBBB

That's 14 ways. Voila!

-t