Can someone please help me understand why the answer to part A of this question is not 6! times 2? The answer given was 2*2*2*2*2*2=64
I think I'm having a problem, in general, of knowing how to replicate the total number of options in a given problem. I don't tend to mess up problems when it comes to differentiating between permutations and combinations, but I often make mistakes when it comes to decidingng whether to use permu/combo OR just multiply the choices/make a decision type tree. Can anyone help me out with this?
Kevin has wired 6 light bulbs to a board so that, when he presses a button, each bulb has an equal chance of lighting up or staying dark. Each of the six bulbs is independent of the other five.
(a) In how many different configurations could the bulbs on the board light up (includ- ing the configuration in which none of them light up)?
GMAT Forum
4 postsPage 1 of 1
- sarahmoore.2009
- Forum Guests
- Posts: 6
- Joined: Tue Jan 01, 2013 10:17 am
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
Re: When to use factorials versus simple multiplication
what will help first, here, is understanding how you think about these problems.
if you're trying to remember "rules" for how to formulate these things, then that's going to be hard.
it's certainly too hard for me; i can't do it.
what i do, instead, is just remember one or two "sample" situations for each thing.
for instance, i remember this specific example:
* The number of ways to arrange 6 books on a shelf (in any order) is 6x5x4x3x2x1 = 6!.
... and i remember this one:
* If there are 6 available toppings for a pizza (and you can't double them), then the total number of ways to make the pizza is 2x2x2x2x2x2 = 2^6 (since there are six "yes/no" decisions in a row).
no way i could think about these as abstract "rules" -- i just don't have the capacity to do that.
but, when i look at this problem, i just notice that each lightbulb is the same as a pizza topping, and, boom! done.
do you have any such canonical examples in mind? if not, make up a "library" of such examples, and then try some combinatorics problems again and see whether you find them easier.
(it's important that you make up the examples in your "library"; don't try to memorize examples written by other people.)
if you're trying to remember "rules" for how to formulate these things, then that's going to be hard.
it's certainly too hard for me; i can't do it.
what i do, instead, is just remember one or two "sample" situations for each thing.
for instance, i remember this specific example:
* The number of ways to arrange 6 books on a shelf (in any order) is 6x5x4x3x2x1 = 6!.
... and i remember this one:
* If there are 6 available toppings for a pizza (and you can't double them), then the total number of ways to make the pizza is 2x2x2x2x2x2 = 2^6 (since there are six "yes/no" decisions in a row).
no way i could think about these as abstract "rules" -- i just don't have the capacity to do that.
but, when i look at this problem, i just notice that each lightbulb is the same as a pizza topping, and, boom! done.
do you have any such canonical examples in mind? if not, make up a "library" of such examples, and then try some combinatorics problems again and see whether you find them easier.
(it's important that you make up the examples in your "library"; don't try to memorize examples written by other people.)
- sarahmoore.2009
- Forum Guests
- Posts: 6
- Joined: Tue Jan 01, 2013 10:17 am
Re: When to use factorials versus simple multiplication
Your response was extremely helpful. Thank you so much!
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
Re: When to use factorials versus simple multiplication
you're welcome.
4 posts Page 1 of 1