Question

How many 4 letter words can be made from the word EXAMINATION

Answer 1

@hartnn , @ganeshie8

Answer 2

@wio

Answer 3

exam ,mint,next,none

Answer 4

a lot.

Answer 5

First split up int distinct groups of letters.

Answer 6

YA , i know the beginning process and everything , the answer is 2454
@wio , just give me the detailed explanation

Answer 7

the three cases , etc

Answer 8

EXAMINATION

E
X
M
T
O

I I
N N
A A

First classify based on number of letters

Answer 9

okay , then

Answer 10

First case is all distinct letters, which is \(^8P_4\)

Answer 11

Second case is 2 distinct letters and then 1 repeated letter

Answer 12

ya , so C(3,1) * C(7,2) * 4factorial ?

Answer 13

I think first you choose 7 distinct letters \(^8C_7\) then you chose 1 repeated letter \(^3C_1\). Assign the distinct letters a position \(^4C_3\) and let the let the repeated letters fall in to their place.

Answer 14

Actually I think I might be a bit wrong on the choosing 7 distinct letters part.

Answer 15

ya , that step is incorrect

Answer 16

:P

Answer 17

huh , had this as a 6 marker on my test today , apparently my teacher had given the same question with "MATHEMATICS" and the students mugged it up

Answer 18

the answer is also same

Answer 19

First choose the repeated letter \(^3C_1\) and then choose the two distinct letters \(^7C_2\) and then assign them sports \(^4C_3\)

That would make sense, right?

Answer 20

ya

Answer 21

For the final step, we would do both 2 repeated letters.
So \(^3C_1\) and \(^2C_1\) gets us the two letters we want.

Assign the first two distinct letters with \(^4C_2\)
Assign the first repeated letter with \(^2C_1\), the last letter falls into place.

Answer 22

why not just C(3,2) * 4fact/2fact*2fact

Answer 23

BTW , Congrats on 99 , last time i saw u were 92

Answer 24

It's the same thing

Answer 25

HMM , OK

Answer 26

and then add , ryte

Answer 27

In fact I definitely should have just said \(^3C_2\)

Answer 28

?

Answer 29

:D

Answer 30

Each case has its steps multiplied, because they are sequential (independent steps)
The cases themselves are added because they are simultaneous (mutually exclusive cases)

Answer 31

ya , that's what i meant :D

Answer 32

thanks bro :D

Answer 33

Cool, make sure it works out to the right answer.

Answer 34

umm , how do i give a testimonial ?

Answer 35

ya , it does

Answer 36

hover over name, then become fan, then testimonial button appears

Answer 37

You just made me 90 in problem solving.

Answer 38

HAHA , it's the least i could do

Answer 39

What answer did you get?

Answer 40

what the actual??

aren't you falsely assuming that every 4-letter combination is a word?