First slide

Theorems of probability

Question

Words from the letters of the word PROBABILITY are formed by taking all letters at a time. The probability that
both B's are not together and both .I's are not together is

Moderate

A

$\frac{52}{55}$
B

$\frac{53}{55}$
C

$\frac{54}{55}$
D

None of these

Solution

$The total number of cases is 11! / 2! \times 2! .$
$The number of$ $favorable cases is [11! / (2! \times 2!)] - 9! Therefore, the required probability is$
$1 - \frac{9! \times 4}{11!} = \frac{53}{55}$

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