The correct option is C 176
We are given the word MISSISSIPPI
Here,
M−1
I−4
S−4
P−2
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.