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Question

Number of words that can be formed by using the 4 letters of the word MISSISSIPPI is

A
192
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B
148
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C
176
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D
164
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Solution

The correct option is C 176
We are given the word MISSISSIPPI
Here,
M1
I4
S4
P2

Case 1: When all the four letters are distinct:-
4P4=4!=24

Case 2: When two letters are repeated:-
the repeated letter can be selected from I,S,P i.e. 3C1 and the remaining two letters can be selected from 3 i.e. 3C2. After selecting these 4 letters we have to arrange them while keep in mind that 2 of them are same.
Number of ways
=(3C1× 3C2)4!2!
=108

Case 3: When one is repeated twice and another one is repeated twice:-
Numbe rof ways
= 3C2×4!2!2!
=18

Case 4: When one is repeated thrice and other is once:-
Number of ways:
=(2C1× 3C1)4!3!
=2×3×4
=24

Case 5: When one is repeated 4 times:-
Number of ways:
= 2C1×4!4!
=2

Total number of 4 letter words formed from the letters of the words MISSISSIPPI can be computed by summing up the result of all these 5 cases.

i.e. 24+108+18+24+2
=176

Therefore total of 176 words can be formed from the letters of the word MISSISSIPPI.

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