Pascals triangle!- questions

Hi i have a few questions i had trouble with, i need some help! here are the questions,

1) Find an equivalent _{n}C_{r }that is the sum of the following. The symmetric pattern. _{44}C_{19 }+ _{44}C_{20
2) }Find an equivalent _{n}C_{r }that is the sum of the following. This is the recursive pattern. _{5}C_{1} + _{5}C_{2 Thanks in advance.}

Re: Pascals triangle!- questions

Re: Pascals triangle!- questions

Quote:

Originally Posted by

**Gurp925** Hi i have a few questions i had trouble with, i need some help! here are the questions,

1) Find an equivalent _{n}C_{r }that is the sum of the following. The symmetric pattern. _{44}C_{19 }+ _{44}C_{20
2) }Find an equivalent _{n}C_{r }that is the sum of the following. This is the recursive pattern. _{5}C_{1} + _{5}C_{2 Thanks in advance.}

I would be tempted to make use of the fact that and seeing what we get upon simplification of your expressions.

Re: Pascals triangle!- questions

I should maybe tell you what the answer key says before i ask for help,

1) 45C20

2) 6C2

Re: Pascals triangle!- questions

And what have you tried so far?

Re: Pascals triangle!- questions

you can do it the following way

nCr=

n C r+1=

therefore

nCr + n C r+1 = =n+1/r+1 nCr

nCr + n C r+1= (n+1/r+1) nCr

Re: Pascals triangle!- questions

Quote:

Originally Posted by

**Gurp925** Hi i have a few questions i had trouble with, i need some help! here are the questions,

1) Find an equivalent _{n}C_{r }that is the sum of the following. The symmetric pattern. _{44}C_{19 }+ _{44}C_{20
2) }Find an equivalent _{n}C_{r }that is the sum of the following. This is the recursive pattern. _{5}C_{1} + _{5}C_{2}

You are expected to know Pascals' equality: