How many different three letter words can be created from the 11 lette

Question

How many different three letter words can be created from the 11 letter word "MISSISSIPPI"?
A.71
B.42
C.53
D.68
E.67

chetan2u · Answer

The letters are: M-1, I-4, S-4, P-2

So the 3-letter words can have
1) All three letters same:
 This will happen when we use three of the same letter. Only I and S are used 3 or more times.  
Possibilities- III or SSS. 2 ways
2) Two letters same and third different: 
 We have four letters that are used 2 or more times.  
a)  Words with a M 
Pick up M,  which is used once, and any of the twos of other 3 in 3C1 ways, and then arrange them in 3!/2! or 3 ways, so ways 1*3C1*3=1*3*3=9. 
Example MSS, SMS, SSM, MPP and so on
b)  Words without M 
Pick up two from the three letters, I, S and P, in 3C2 ways. 
Use one of them two times and other once for example IIS. 
Since two are of same kind, the ways these three letter can be arranged is 3!/2! or 3 ways. 
But we will have two cases, as each can be used twice. Example IIS, SSI etc. 
So, 3C2*2*3!/2!=18
3) All letters different 
Choose any 3 from given 4 letters and arrange them in 3! ways. So, 4C3*3!=4*3*2*1=24

Total 24+18+9+2=53

C

LaveenaPanchal · Answer

Experts,

Please advise if this approach is ok..

We have 4 letters M (1) - I(4) - P(2) - S(4)

Total possible 3 letter number if all the letters without restriction of number of letters is 4 x 4 x 4 = 64

Form these we need to remove some options since M not possible with 2 Ms and P not possible with 3 Ps.

(1) 3 same letter words MMM & PPP --- 2
(2) 2 Letter words with 2 Ms - 1 (M) x 1(M) x 3(any one of I,S,P) x 3 (possible placements i.e, 3rd letter other than M can be placed 1st, 2nd or 3rd place)---Total 9

So the answer is 64 - 2 -9 = 53.

chetan2u · Answer

You are perfectly fine with your approach. This is another way to look at the question. Good job.

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How many different three letter words can be created from the 11 lette

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How many different three letter words can be created from the 11 lette

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