Question

How many seven letter words can be formed without repetition from the letters of the word INCLUDE.

That have the letters N and D separated by exactly two letters

Answer 1

I would be able to do this, but that last part threw me off

Answer 2

lol i got the first part already its just 7!

Answer 3

I don't even get the last part. This is a dumb question

Answer 4

N and D are separated by 3 letters, not two

Answer 5

tell that to my text book lol

Answer 6

thats isn't relevant because all the letters can rearranged there not in order

Answer 7

Oh okay. Well I think you may have to do this by hand to figure it out

Answer 8

So, I guess the question is, from the letters INCLUDE, how many ways can n and d be separated by 2 letters?

Answer 9

yes I'm sorry i didn't write it correctly

Answer 10

does it assume that letters cannot be repeated?

Answer 11

Yes, no reps

Answer 12

But I'm not so confident I can do it

Answer 13

well i have the answer i just don't know how to do it

Answer 14

do you reckon you could have a go at it?

Answer 15

What's the answer?

Answer 16

960

Answer 17

Hmm, okay

Answer 18

Yeah, clearly doing it by hand is not an option

Answer 19

lol omg i hate probability

Answer 20

I can't help you with this. It is beyond me

Answer 21

i see well thanks for your effort

Answer 22

I might post an explanation later.....we'll see

Answer 23

we can do this

Answer 24

yay

Answer 25

N _ _ D _ _
_N _ _ D _
_ _ N _ _ D

Answer 26

and of course 3 more with the N and D switched.

Answer 27

so how many if it looks like
N _ _ D _ _
?

Answer 28

you have 4 slots to fill in so 4!

Answer 29

and likewise for
_ N _ _ D _
and for
_ _ N _ _ D

Answer 30

each of these have 4! ways

Answer 31

so unless i am totally off we have
\[6\times 4!\] ways of doing it, by counting. does that look reasonable?

Answer 32

i get 144

Answer 33

unfortunately its 960 lol

Answer 34

damn hold on let me think!

Answer 35

ok lol:)

Answer 36

oh because i can't count!

Answer 37

there are 7 letters not 6!

Answer 38

i am a moron yikes. it is not
\[6\times 4!\] it is
\[8\times 5!\]

Answer 39

if i could count correctly it would be clear so lets start again. we have 7 letter. could look like
N _ _ D _ _ _
_ N _ _ D _ _
_ _ N _ _ D _
_ _ _ N _ _ D

Answer 40

or the same with the N and D switched.

Answer 41

yep

Answer 42

so 8 possibilities all together

Answer 43

each of which has 5! arrangements because you are filling 5 slots

Answer 44

so the answer is
\[8\times 5!\]

Answer 45

now i hope this is what you have

Answer 46

thank you so much ur awesome:)

Answer 47

960 right?

Answer 48

yep thats correct :)

Answer 49

yes i scrolled up so it is right

Answer 50

we could have done it quickly if i knew how to count to 7 instead of 6
don't you hate combinatorics?

Answer 51

yes i do lol i hate probability in general would much rather do calculus:)

Answer 52

Yeah, I figured it out too.