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Words from the letters of the word PROBABILITY
are formed by talking all at a time.The probability
that both B’s are together & both I’s are together is
- a)1/55
- b)2/55
- c)4/155
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Words from the letters of the word PROBABILITYare formed by talking al...
Total sample space =11!/2!×2!
Now, put both I'S and both B'S in a box and consider them two different words and except them we have 7 other words . Therefore, total different words =9
no.of favourable event=9!
P(E)=9!/(11!/2!×2!) =4/110=2/55
Now, put both I'S and both B'S in a box and consider them two different words and except them we have 7 other words . Therefore, total different words =9
no.of favourable event=9!
P(E)=9!/(11!/2!×2!) =4/110=2/55
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Words from the letters of the word PROBABILITYare formed by talking al...
Understanding the Problem
To find the probability that both B's and both I's in the word "PROBABILITY" are together, we need to analyze the arrangement of letters in the word.
Step 1: Count Total Arrangements
- The word "PROBABILITY" has 11 letters.
- The letters consist of: P, R, O, B, A, B, I, L, I, T, Y.
- The total arrangements are calculated considering the repetitions of B's and I's:
Total arrangements = 11! / (2! * 2!) = 11! / 4
Step 2: Treating B's and I's as Groups
- To find arrangements with both B's together and both I's together, we can treat each pair as a single unit:
- Treat "BB" as one unit.
- Treat "II" as another unit.
- Thus, we have the units: BB, II, P, R, O, A, L, T, Y. This gives us 9 units in total.
Step 3: Arranging the Units
- The arrangements of these 9 units (BB, II, P, R, O, A, L, T, Y) are:
Arrangements = 9!
Step 4: Calculate the Probability
- Now, we need to calculate the probability that both B's and I's are together:
Probability = (Arrangements with BB and II together) / (Total arrangements)
- Therefore,
Probability = (9!) / (11! / 4)
- Simplifying this gives:
Probability = (9! * 4) / 11!
- After simplification, we find that the probability equals 2/55.
Final Answer
Thus, the correct answer is option 'B': 2/55.
To find the probability that both B's and both I's in the word "PROBABILITY" are together, we need to analyze the arrangement of letters in the word.
Step 1: Count Total Arrangements
- The word "PROBABILITY" has 11 letters.
- The letters consist of: P, R, O, B, A, B, I, L, I, T, Y.
- The total arrangements are calculated considering the repetitions of B's and I's:
Total arrangements = 11! / (2! * 2!) = 11! / 4
Step 2: Treating B's and I's as Groups
- To find arrangements with both B's together and both I's together, we can treat each pair as a single unit:
- Treat "BB" as one unit.
- Treat "II" as another unit.
- Thus, we have the units: BB, II, P, R, O, A, L, T, Y. This gives us 9 units in total.
Step 3: Arranging the Units
- The arrangements of these 9 units (BB, II, P, R, O, A, L, T, Y) are:
Arrangements = 9!
Step 4: Calculate the Probability
- Now, we need to calculate the probability that both B's and I's are together:
Probability = (Arrangements with BB and II together) / (Total arrangements)
- Therefore,
Probability = (9!) / (11! / 4)
- Simplifying this gives:
Probability = (9! * 4) / 11!
- After simplification, we find that the probability equals 2/55.
Final Answer
Thus, the correct answer is option 'B': 2/55.
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Words from the letters of the word PROBABILITYare formed by talking all at a time.The probabilitythat both B’s are together & both I’s are together isa)1/55b)2/55c)4/155d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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