# Binominal Expanion on Calculators (Casio)Watch

#1
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?

Michail
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12 years ago
#2
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.
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12 years ago
#3
(Original post by 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?

Michail
10C4:

10 SHIFT nCr 4 = [get 210]

Need a new manual?

Aitch
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#4

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

Michail
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12 years ago
#5
(Original post by MichailZ)

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
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#6
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
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quote
12 years ago
#7
(Original post by 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.
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#8
OK I get it now, thank you very much for your help Aitch!

Michail
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#9
Sorry to bother again, can you help me out with this:

I know that [x]nCr[2] = 28 . How do I find X?

Thanks

Michail
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12 years ago
#10
(Original post by MichailZ)
Sorry to bother again, can you help me out with this:

I know that [x]nCr[2] = 28 . How do I find X?

Thanks

Michail
x!/2(x-2)!=28
x!=56(x-2)!
x(x-1)(x-2)!=56(x-2)!
x(x-1)=56
x=8
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#11
Thank you! That cleared things up a lot... binomial expansion is the most confusing topic in the whole of Core Mathematics books...

Michail
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