In how many ways can 2 singers be selected from 10 who came to audition?

- anonymous

In how many ways can 2 singers be selected from 10 who came to audition?

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- amistre64

10 for the first spot, and 9 left for the second spot = 10*9, or 10P2

- anonymous

45

- anonymous

or 10 "nCr" 2 = 45

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## More answers

- amistre64

good idea, wrong application i believe

- amistre64

this isnt a nCr, its an nPr

- anonymous

i don't understand how it's not 90, because that's what i did to. how do I knew when i can and cannot use that process amistre did?

- anonymous

know*

- amistre64

whenever you have to pick from a number of applicants, its P for "pick" in my eyes

- amistre64

whenever the order doesnt matter, then its groups that count. nCr for groupings

- amistre64

10 Pick 2 = 10P2 = 10*9 = 90

- anonymous

This should be \(\binom{10}{2} = 45 \)

- anonymous

Fair enough, I've never had to use P... Whenever I've done this in stats (ie with Binomial distribution) it's been nCr...

- anonymous

How does the order matter in this, isn't it just saying 2 singers?

- amistre64

i could be wrong, depends on how you interpret the question

- amistre64

if you have 2 people that are auditioning; then you need to pick 1 for the 1st and 1 for the 2nd

- anonymous

the answer is 45 i know that for sure, just trying to understand

- amistre64

joe then sally is a different order than sally then joe

- anonymous

oh okay

- anonymous

No, as there are many different ways of picking 2 people from a bag of 10, which is different from picking 10 from a bag of 2...

- anonymous

amistre,
>>In how many ways can 2 singers be selected from 10 who came to audition?
"selected" is the keyword here.

- amistre64

i can see that interpretation as well :)

- anonymous

But unfortunately 10P2 doesn't seem to be the correct interpretation here. :(

- amistre64

right, then if it aint 90, go 45 ;)

- anonymous

how do i put this into a calculator? its not 10!2 is it because that doesn't work

- amistre64

10P2/2!

- anonymous

the button that looks like nCr you would type 10 'nCr' 2

- amistre64

sooo
10!/2!(10-2)! perhaps?

- anonymous

which gives you an answer of 45.

- anonymous

or the factorial method, yes!

- amistre64

10*9*8*7*6*5*4*3*2
------------------
8*7*6*5*4*3*2*2

- anonymous

sorry i totally forgot how to do this. when i click permutations it puts in nPr() on the screen. where do i put the 10 and 2? and why is it 10 and 2 instead of 2 then 10?

- anonymous

It is 10C2 because 10 (n) is the number of values and 2 (c) is the number you are choosing.

- anonymous

I don't know how you would do it in that format, you know your calculator best.

- anonymous

so its combination or permutation?

- anonymous

ok its a combination because the order does not matter. i did this and got 45.

- anonymous

That's right.

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