Discrete Math 2-Tutorial 6- Combinations w/repetition Part 1

Introduction to Combinations with repetition and example or runs.

[coursehack]

y is a replacement for x-1 (we're trying to ensure that there will always be a Head or Tale at that position.

since all we care about is the run... we must place at least 1 for x_1 and at least 1 for x_3; that way we have guaranteed that the run will be HTH... we dont care about where the other 2 heads go.

does that help?

[jojomf]

Hello there, I'm not very sure either but looking at for some time. My understanding is to treat x1 and x2 as sets such that x1 and x2 include 0, 1, 2, 3, 4. Now, he subtracts 1 from both side of the equation to get rid of the inequality x1 >= 0, so by subtracting it, he has now change the inequality to x1 >= -1 which is equivalent to x1 > 0 because we established to restrict our domain to only positive integers. Hope that helps :-)

[StexeGod]

Pro tip for making examples: use different numbers (not 2 items chosen in 2 ways) because then people new to the subject will not know which number goes to what part. Also, don't use examples where you need to learn new things (like what a run means).

[rrockzilla]

How can x1 be greater than or equal to zero? If it were 0, there would be only two runs of 6 tails and 4 heads. I am really confused.

[gigiisamonkey]

i don't think I'm understanding the -1 thing correctly. if x>=0 and y=(x-1) then x can be 0 in which case y= -1. So this certainly doesn't guarantee y>0. I'm really confused.

[zikangzhao]

why you need sub 1 from both side of equation? i dont get it :( can you explain that :D

[Sublme]

This is doing nothing but confusing me... I'm taking two different classes right now (Finite Math & Statistics) and neither of my professors gave me an equation with 1's in it. Also, the lifeless girl thing is HELLA creepy. What does that have to do with anything?

[forresta]

just wondering about the lifeless girl thing, kinda wierd