Binominal Expanion on Calculators (Casio)

Hi,

Can someone please explain to me how to use the nCr and nPr keys on Casio scientific calculators for Binominal expanison. Not the Binominal expansion, but how to do it on the calculator?

Thank you in advance,

Michail

Reply 1

samd

10

The nCr button provides you with the coefficients for the binomial expansion. It really means out of n things you are Choosing r of them, how many ways can it be done? You will see how this relates to the binomial expansion if you expand a few (ax + b) brackets out. But that is not of critical importance.

You use it like this:

[ Power] [ nCr ] [ Term No. ]

So if you were expanding (ax + b)⁵:

The power is 5 and the term number is whichever term you are interested in. Importantly the first term is always zero (as in that term the b is raised to the power zero given you choose to use descending powers of x).

So the coefficients of the expansion above are:

[5] [ nCr ] [0] = 1
[5] [ nCr ] [1] = 5
[5] [ nCr ] [2] = 10
etc.

Note that it will always be symetrical i.e. 5C1 = 5C4, but you should know this about the Binomial anyway.

Reply 2

Aitch

2

MichailZ

Hi,

Can someone please explain to me how to use the nCr and nPr keys on Casio scientific calculators for Binominal expanison. Not the Binominal expansion, but how to do it on the calculator?

Thank you in advance,

Michail

10C4:

10 SHIFT nCr 4 = [get 210]

Need a new manual?
http://world.casio.com/calc/download/en/manual/

Aitch

Reply 3

MichailZ

OP

Thanks alot! What about nPr?

And also thanks for the manual. There are things I didn't know my calculator could do...

Michail

Reply 4

Aitch

2

MichailZ

Thanks alot! What about nPr?

And also thanks for the manual. There are things I didn't know my calculator could do...

Michail

Same technique, but the key next door! (I'm assuming that the keys whose SHIFT functions are nCr and nPr are next to each other on most (all?) models.)

Aitch

Reply 5

MichailZ

OP

Yes, they are next to each other, but do you know what is the answer if I put in [X] nPr [Y] = Z, what is Z then, what does doing that give me (i.e. nCr gives a particular term in the Pascals Triangle and nPr?

Thanks

Michail

Reply 6

Aitch

2

MichailZ

Yes, they are next to each other, but do you know what is the answer if I put in [X] nPr [Y] = Z, what is Z then, what does doing that give me (i.e. nCr gives a particular term in the Pascals Triangle and nPr?

Thanks

Michail

Example:
3 nPr 3 = 6

meaning -
there are 6 arrangements of the numbers 1,2,3 without any duplication of numbers

123
132
213
231
312
321

- allocations of 3 people to 3 jobs: 6 possible arrangements, etc.