Combination/Permutation Question

[baily106]

Hello,

I am referring to question #9 on page 297 of The Official Guide Book. The question asks "from a box of 10 lightbulbs, you are to remove 4. How many different sets of 4 lightbulbs could you remove?" Why is the answer 210? Does it have to do with the fact that we're not considering individual bulbs, but instead sets?

Thanks.

[kwame.appau]

Let me help reduce the workload of Tommy

To solve this question. lets assume that there are 4 slots. each bulb will have one slot.
-The first bulb has 10 ways to be selected, the second has 9, the third has 8 and lastly the fourth has 7 ways of being selected.
-Hence 10x9x8x7. now lets divide this by the number of ways they can be arranged which is 4!
-(10x9x8x9)/4!= 210

[tommywallach]

Great explanation from Kwame here!

I'm not sure I understand your original question, to be honest. We are always considering individual lightbulbs, even when considering how many ways they can be arranged into sets.

Never forget that, when doing combinatorics, there is actually no difference between picking up a bunch of stuff at once, or doing the same thing separately (i.e. picking 4 lightbulbs one by one or picking up 4 at the same time). The only exception would be if there were replacement (i.e. you pick up a lightbulb, then replace it, then pick again).

Let me know if this all makes sense now.

-t

[baily106]

It makes sense; thank you!

[tommywallach]

Glad to help! (As is Kwame!)

-t