First slide

Combinations

Question

The number of different words that can be formed with the letters of the word 'MISSISSIPPI', is

Moderate

A

$\frac{11!}{4! 4! 2!}$
B

$\frac{11!}{4! 4!}$
C

$\frac{11!}{4! 2!}$
D

none of these

Solution

There are 11 letters in the given word, of which 4 are $S^{'} s, 4$ are $I^{'} s$ and 2 are P's. So, total number of words is the number of arrangements of 11 things, of which 4 are similar of one kind, 4 are similar of second kind and 2 are similar of third $\frac{11!}{4! 4! 2!}$
Hence, the total number of words $= \frac{11!}{4! 4! 2!}$

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