Perms and Combs (1 Viewer)

[Archman]

weak induction: normal one you learn at skool, eg, assume finite previous ones are true, prove next is true.
strong induction (im assuming thats what you wanted to know about): i don't think you need it for hsc purposes, assume all previous ones are true, eg from 1 to n, and prove n+1 is true.

 

[nit]

Actually, you needed strong induction for our (SGS) trial this year, though we were taught it in the lead-up...can't remember the question exactly but it had a 7/4 in the inequality. Yeh, I don't think it was required for HSC, but it's probably a good thing to know and practise.

 

[withoutaface]

You use fibonacci sequences in 4u sometimes, that involves strong induction doesn't it?

 

[Slidey]

*slaps his head at writing 'storm' instead of 'strong'*

Thanks, Ivan. That helps a lot.

 

[velox]

2 Questions

In how many ways can 3 men, 3 women, and 3 boys be arranged in a row if three boys are to remain together?

Find the number of arrangements of the letters of the word 'pencils' if (a) e is next to i

thanks

 

[Estel]

7!3! as you basically have 7 entities (the 3 boys must be together) and then you can arrange the boys within themselves(pardon the poor language there).

Similarly 6!2! for your other q.

 

[velox]

for the 2nd one, isnt there 7 letters in 'pencils' so it wouldnt it be 7-2=5 so 5! * 2! ?

edit now i c.... 7 letters, then itll become 6 as there are the 5 letters plus this group, then the arrangements of the i and the e will be 2! = 2. thanks estel

 

[Slidey]

There are 7 letters in pencils, but the viable entities are

p, n, c, l, s and ei OR ie. You treat the permutations of i and e as one single entitity, as they essentially are one entity - they are always together.

So we have 5 letters plus one double letter entitity = 6, so take the factorial of 6. And obviously you take factorial 2 for the permutations of i and e.

6!2!

EDIT: I have a habbit of only half-reading posts before replying. Sorry.

 

[velox]

ok, its 'habit' lol .thanks anyway

 

[*zara*]

induction is heaps easier than parametrics that seriously doesnt get thru ma head! i seriously dont understand anything to do with parabolas we juz dont get along !!!!

 

[velox]

Hmm i hope induction will be easy by the time my assesments come. I hate the inequalities......

 

[Trefoil]

Practice makes perfect...

http://www.geocities.com/mathematicsplus/y11_pre_maths_ext1_worksheet_induction.pdf

http://www.geocities.com/mathematicsplus/y11_pre_maths_ext1_worksheet_harder_induction.pdf

 

[velox]

oh cool thanks!