Binomial Theorem and Probability Help please! (1 Viewer)

[Espy25]

By far my weakest topics, I just don't get those sigma notation thingos and like those terms questions where its like n^Ck / (n+1)! or something like that?

And probability, any tips on when to use Perms and when to use Combinations? I usually just end up using like 6!/2! or just fractions and n!s

Please help! :S Any general way to look into these problems?

 

[Skeptyks]

mayb post a few specific questions?

 

[Fakeuser]

Permutations - where order is important. For example, if I was to arrange 10 people in a straight line, it would matter how I arranged them and therefore you'd use permutations.

To explain it differently, imagine I had to arrange the letters ABCD in a line. I could do so in quite a few ways: ABCD ACDB ABCD BACD ... etc.

Combinations, however, are where order is not important. Therefore if I had to arrange ABCD in a line, there would only be one way of doing so as in combinations ABCD ACDB ABCD BACD ... etc. are considered the same thing.

An example of a combination style question is where you have to SELECT a committee of say 5 people from 10 people. If I was to choose any random 5 people, that would be ONE combination. It doesn't matter what order I have those 5 people in, so it is a combination.

In summary - if you see ARRANGEMENT in the question, it's a permutation (99% of the time) and if it says SELECTION it's a combination. Obviously they can use other words so you'll just have to judge for yourself whether order is important or not.

 

[Espy25]

Permutations - where order is important. For example, if I was to arrange 10 people in a straight line, it would matter how I arranged them and therefore you'd use permutations.

To explain it differently, imagine I had to arrange the letters ABCD in a line. I could do so in quite a few ways: ABCD ACDB ABCD BACD ... etc.

Combinations, however, are where order is not important. Therefore if I had to arrange ABCD in a line, there would only be one way of doing so as in combinations ABCD ACDB ABCD BACD ... etc. are considered the same thing.

An example of a combination style question is where you have to SELECT a committee of say 5 people from 10 people. If I was to choose any random 5 people, that would be ONE combination. It doesn't matter what order I have those 5 people in, so it is a combination.

In summary - if you see ARRANGEMENT in the question, it's a permutation (99% of the time) and if it says SELECTION it's a combination. Obviously they can use other words so you'll just have to judge for yourself whether order is important or not.

Thank you!

About binomials

And stuff, I'm confused in those sigma notation questions where you differentiate both sides or cancel out eg. Also those questions where it's like find x^n terms in ratios of one another. eg. find ratio of coeff of x^2 to x^5.

For example, last question of HSC 2011 q7 and HSC 2010 q7