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6.Permutation and Combination
hard
How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent $?$
A
$8.^6C_4$
B
$6.7. ^8C_4$
C
$6.8. ^7C_4$
D
$7. ^6C_4. ^8C_4$
(AIEEE-2008)
Solution
Given wird is $MISSISSIPPI$
Here $I=4$ times, $5-4$ times, $P-2$ times, $M=1$ time
$\because$ Required number of words $=8 C_{4} \times \frac{7 !}{4 ! 2 !}$
$\Rightarrow 8 C_{4} \times \frac{7 \times 6 !}{4 ! 2 !}$
$\Rightarrow 7.8 C_{4} .6 C_{4}$
Standard 11
Mathematics