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Word from the letters of the word PROBABILITY are formed by ta

Question

Word from the letters of the word $PROB A B I L I T Y$ 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

52/55

53/55

54/55

none of these

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Word from the letters of the word

PROB A B I L I T Y

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

7 mins ago

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7 mins ago

Text solutionVerified

PROB A B I L I T Y

Let us treat

2 B^{'} s

and

2 I^{'} s

together.

∴

Total letters know

7 + 2 = 9

\Rightarrow

no. of ways

= 9! \times 2

Total ways

= \frac{11 !}{2 ! 2 !}

So probability

= 1 - \frac{2 \times 9 !}{11 !} \times 2! \times 2!

= \frac{53}{55} .

Hence, the answer is

\frac{53}{55} .

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Question Text	Word from the letters of the word $PROB A B I L I T Y$ 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
Answer Type	Text solution:1
Upvotes	150