Find the number of permutations in the word "computer"

Question

amistre64 · Answer

how many letters in the word?

anonymous · Answer

8

amistre64 · Answer

and, are any of them repeated?

anonymous · Answer

no

amistre64 · Answer

then all we have is 8! ways to arrange them.

anonymous · Answer

really? does that mean that the answer is 8?

amistre64 · Answer

no, it means the answer is 8-factorial

anonymous · Answer

yeah exactly I think I need to find the fraction first and then the main answer

amistre64 · Answer

the fraction ends up as 8!/0!  which is just 8! ....

anonymous · Answer

that is greaat thank you! would you help me with another question?

amistre64 · Answer

depends on the question i spose,  i only have a limited amount of knowing each day before the dementia sets in :)

anonymous · Answer

haha okay so: How many ways can you purchase 5 CDs if there are 6 to choose from, 2 cassettes if there are 5 to choose from, and 4 DVDs if there are 8 to choose from?

amistre64 · Answer

for a collection of n objects, where we want choose them in k ways.  then the different ways are just nCk.  which is equal to nPk/k!

anonymous · Answer

ok? so how would that go?

amistre64 · Answer

lets take the cds ... there are 6 to choose from, and we want 5.  that tells us there are 6C5 ways to select them.

solomonzelman · Answer

Looking at the initial post,

8 nPr 1  +  8 nPr 2  + 8 nPr 3 + .... + 8 nPr 8 .

solomonzelman · Answer

If you are choosing ANY amount of letters from "computer" ... idk

anonymous · Answer

Solomon you are solving my first question right? I think the answer to that one is 8

anonymous · Answer

now I need to figure out: How many ways can you purchase 5 CDs if there are 6 to choose from, 2 cassettes if there are 5 to choose from, and 4 DVDs if there are 8 to choose from?

amistre64 · Answer

the counting rule for duplicates is:$$\frac{n!}{a!b!c!...k!}$$which may be useful for the 2nd stuff

amistre64 · Answer

otherwise im thinking:

$$(n_1Ck_1)*(n_2Ck_2)*(n_3Ck_3)$$

anonymous · Answer

I think I have to use the first one

amistre64 · Answer

the first one is iffy to me,  it counts the number of ways to permute all the objects,  not subsets of them.  at elast in my mind

amistre64 · Answer

otherwise we can tree it as:|dw:1402072347763:dw|