Question

I need help with this Probability problem.
How many 4 letter arrangements can be made from the word ELEMENTARY?

Here's my solution (Using Cases)
(There are 3 E's and 7 distinct letters)
Case1. No E _ _ _ _ (7x6x5x4) = 840 ways

Case2. 1 E
E _ _ _
_ E _ _
_ _ E _
_ _ _ E
so that makes it (7x6x5x4) = 840 ways
Case 3. 2 E's
E E _ _
E _ E _
E _ _ E
_ E _ E
_ _ E E
(7x6x5) =210
Case 4. 3 E's
E E E _
E _ E E
E E _ E
E E E _
(7x4) = 28
Add them all together
840 + 840 +210 + 28 = 1918 ways
But the reviewer where I got this questions says it's 1960 ways...

Answer 1

yeah its 1960 ways

Answer 2

@bhaskarbabu can you tell me what I missed in my sol'n?

Answer 3

actually i have done in another process
can i explain u that one

Answer 4

please do

Answer 5

okay i got ur process

Answer 6

with 2 E's u should get 252 ways

Answer 7

suppose u have selected 2 E's already
then u have to select other two letters from LMNTARY
u can select the other two in 7C2 ways
now u should arrange these four letters
this can be done in 4!/2! ways
now total ways is equal to 7C2 * 4!/2! = 252

Answer 8

you missed this:

_EE_

Answer 9

yes..that's the only thing you missed in your solution.

Answer 10

this corrects it..

otherwise,,permutation does it easily..

ans is 10P4 / 3!

Answer 11

@shubhamsrg I did XD
@bhaskarbabu oh right :)) thanks for reminding me about that

Answer 12

welcome:)