bit of a combination/permutation type question (1 Viewer)

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1)
how many ways can you choose 7 different numbers, no two consecutive from {1,2,3,...,50}

2) Let a_n be the number of ways to make change for n cents, using 5c, 10c,50c,$1 and $2 coins. Find the generating function for a_n

 

[turtle_2468]

I know the first one...
busy right now, but if no one posts within a day bump it and I'll post up.
Second one: Think about later.
Ohh.. I'm assuming you don't know the answer.. if you do, get cracking on it guys who read these posts!

 

[Templar]

For the first, I'm thinking 50C7-49*48C5. Could be wrong though.

Second one could be done with a recursive formula, but solving the characteristic polynomial could be messy.

 

[Archman]

bored, plus templar is clueless, so
1. (50+1-7)C7
2.1/(1-x^5)*1/(1-x^10)*1/(1-x^50)*1/(1-x^100)*1/(1-x^200)

 

[turtle_2468]

man.. no one learnt anything from my recursions lectures did they..

 

[...]

haha

too late now

i submitted my work in
i got what archman got for question 2

whereas i couldn't finish off q1
oh well, i shall wait for the solutions when they post it up

 

[Templar]

bored, plus templar is clueless, so
1. (50+1-7)C7
2.1/(1-x^5)*1/(1-x^10)*1/(1-x^50)*1/(1-x^100)*1/(1-x^200)

Go back to retirement.

 

[turtle_2468]

we're like pieces of nostalgia you get every so often...

we pop up for a second, then you blink and we're gone again

 

[Templar]

we're like pieces of nostalgia you get every so often...

we pop up for a second, then you blink and we're gone again

If only that happened in real life (not you, just Archman).

 

[nit]

lol @ Archman

 

[香港!]

wow, Archman back!! he haven't post for sooooooo long!!

 

[...]

1)
how many ways can you choose 7 different numbers, no two consecutive from {1,2,3,...,50}

here is the answer if anyone is interested;