Question

How many 6 letter words can you create from the word ELEMENTARY?

Note: The words do not have to be legitimate

Answer 1

INFINATE!

Answer 2

no...not really...there are finite letters

Answer 3

ik

Answer 4

36

Answer 5

What haha

Answer 6

words

Answer 7

yes exactly

Answer 8

too bad you took it back though

Answer 9

7C6 * 6! + 7C5 *6! + 7C4 * 6!/2! + 7C3 *6!/3!

Answer 10

it's a pretty big number

Answer 11

sadly...no @sauravshakya

Answer 12

do you know the answer?

Answer 13

yes

Answer 14

8015

Answer 15

i don't think so...how did you get it? i may be wrong

Answer 16

\[_7P_6+ _7P_5+\frac{_7P_4}{2!}+\frac{_7P_3}{3!}\]

Answer 17

I believe I am wrong now....give me a sec

Answer 18

34650

Answer 19

Can I ask a question?

Answer 20

it's still too small...let me check

Answer 21

I should prob write this down instead of just typing on my calc :)

Answer 22

hmm actually that was too big

Answer 23

First tell me how many 6 letter words can u create from a,b,c,d,e,f

Answer 24

that would be 6! yes?

Answer 25

since none repeated

Answer 26

And how many 6 letter word from a,b,c,d,e,f,g

Answer 27

now I'm getting sauravshakya answer...though I did it a different way

Answer 28

Isnt it 7C6 *6!

Answer 29

suppose so..yes

Answer 30

Then what is wrong with my answer?

Answer 31

it's not the same as your example

Answer 32

I took four cases with no e , 1 e , 2 e and 3e

Answer 33

what did you do for no e?

Answer 34

7C6*6!

Answer 35

for 1 e?

Answer 36

7C5 *6!

Answer 37

@lgbasallote ???

Answer 38

36960 is correct (what sauravshakya got)

though I wrote it as

\[\sum_{x=0}^{3} {_7P_{6-x}}{6\choose x}\]

Answer 39

It can also be 8C6 *6! + 8C5 *6!/2! + 8C4*6!/3!

Answer 40

what about 2 e?

Answer 41

@sauravshakya

Answer 42

7C4 * 6!/2!

Answer 43

ahh we had different answers in the 2 e

Answer 44

i think you should divide that by 4...

Answer 45

>> A=perms([1 2 3 4 5 6 7 8 8 8]);

>> length(unique(A(:,1:6),'rows'))
ans = 36960

Answer 46

using octave

Answer 47

wait...it seems i made a mistake in my solution...let me recheck

Answer 48

yes. it's 46960

Answer 49

36*

Answer 50

octave would not lie ;)

Answer 51

a simpler looking solution though is \[7! + 6C1 \times 7P5 + 6C2 \times 7P4 + 6C3 \times 7P2\]

Answer 52

you fix your 7P2 (make it 7P3) then you have the solution I gave above

Answer 53

yeah should be 7P3