First slide

Permutations

Question

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

Moderate

A

$8 \cdot^{6} C_{4} \cdot^{7} C_{4}$
B

$6 \cdot 7 \cdot^{8} C_{4}$
C

$6 \cdot 8 \cdot^{7} C_{4}$
D

$7 \cdot^{6} C_{4} \cdot^{8} C_{4}$

Solution

Other than S, seven letters M, I, I, I, P, P, I can be arranged in $\frac{7!}{2! 4!} = 7 \cdot 5 \cdot 3 .$
Now four S can be placed in 8 spaces in $^{8} C_{4}$ ways.
Desired number of ways $= 7 \cdot 5 \cdot 3 \cdot^{8} C_{4} = 7 \cdot^{6} C_{4} \cdot^{8} C_{4}$ .

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