Question

STATISTICS.... Please HELP...
I really do not understand this......

How many different 10 letter words (real or imaginary) can be formed from the following letters?

H, Y, H, T, X, X, Y, G, A, X

Answer 1

hint: multinomial coefficient

Answer 2

Unfortunately, I don't know what that means either. It's my 1st time taking stats & it's online.

Answer 3

which numbers repeat and how often do they repeat?

Answer 4

H, Y, H, T, X, X, Y, G, A, X

H-2
Y-2
T-1
X-3
G-1
A-1

Answer 5

so the number of arrangements is

\[\frac{10!}{2!2!1!3!1!1!}\]

Answer 6

ok, so, that's step 1.

Answer 7

I saw this set up, then I saw n with small k. What does that mean?

Answer 8

?

\[_nC_k\]

Answer 9

did they give a definition for that?

Answer 10

usually that is for a sequence

Answer 11

\[n_1n_2\cdots n_k\]

Answer 12

Nope.
Once I have the above set up (that you have), how do I work that out?

Answer 13

Yes, that right there, that you just posted. What does that mean?

Answer 14

that is a way of counting when you have k groups and in each group i you have \(k_i\) objects.

\[n_1n_2\cdots n_k\] is the number of ways you can pick one object from each group

Answer 15

for example if you have 5 shirts, 3 pants and 4 pairs of shoes...the number of outfits you can make is \(5\times3\times4\)

Answer 16

ok

Answer 17

Ok, so for the above problem,
H-2
Y-2
T-1
X-3
G-1
A-1
I would do 2x2x1x3x1x1=12 ?

Answer 18

What do I do with the 10! on top

Answer 19

no they have to be factorials ...

\[2!\times2!\times1!\times3!\times1!\times1!\]
for the denominator

Answer 20

\[2!\times2!\times1!\times3!\times1!\times1!\]
\[=2\times2\times1\times6\times1\times1=24\]

Answer 21

\[10!=10\times9\times8\times7\times6\times5\times4\times3\times2\times1=3628800\]

Answer 22

ok. I am using the 10 because there are 10 alphabets. Multiply going in descending order.

ok, so my numerator 3628800
and my denominator is 24

No,do divide theses?

Answer 23

yes you need to divide the two numbers

Answer 24

151,200 is my answer

Answer 25

good

Answer 26

Do you have a min, and I can try another one