Question

What is the probability that four S's come consecutively in the world 'MISSISSIPPI'

• A. $\frac{4}{165}$
• B. $\frac{16}{165}$
• C. $\frac{12}{165}$
• D. $\frac{5}{165}$

Answer 1

Answer: (A)

$\frac{4}{165}$

Total number of letters in $MISSISSIPPI=11$ permutation are $4$ of one kind $\left(S\right)$,
$4$ of others kind $1$, $2$ of a third kind $\left(P\right)$ and $1$ of fourth kind $\left(M\right)$
So exhaustive case $=\frac{\left(11\right)!}{4!4!2!1!1!}$

After arrangement of $SSSS$ $4S^{\prime }s$ remaining are $7$ letters of $MIIIPPI$
i.e., of $4$ of one kind $1$, $2$ of other kind $\left(P\right)$ and $1$ fourth kind $\left(M\right)$
so favorable case $=\frac{7!}{4!2!1!1!}$
$\therefore$ Probability of ($4S^{\prime }s$ consequently) in $MISSISSIPPI$
$=\frac{\frac{\left(11\right)!}{4!4!2!1!1!}}{\frac{7!}{4!2!1!1!}}=\frac{8\times 7!\times 4!}{11!}=\frac{4}{165}$