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Find the probability that in a random arrangement of the letter of words in the word ‘PROBABILITY’ the two I’s come together.
- a)2/11
- b)1/11
- c)3/11
- d)4/11
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Find the probability that in a random arrangement of the letter of wor...
Total outcomes = 11!/(2!*2!)
favourable outcomes = (10!*2!)/(2!*2!)
p = 2/11
favourable outcomes = (10!*2!)/(2!*2!)
p = 2/11
Most Upvoted Answer
Find the probability that in a random arrangement of the letter of wor...
In order to calculate the probability, we need to determine the total number of possible arrangements and the number of favorable arrangements.
The word "arrangement" has 11 letters, but two of them are repeated (R). Therefore, we have a total of 10 distinct letters.
The total number of possible arrangements of these 10 letters is 10!.
Now, let's consider the favorable arrangements. We want to find the probability that the two R's are together (RR).
To calculate this, we can treat the two R's as a single letter. This reduces the problem to arranging 9 distinct letters (A, A, N, G, E, M, T, N, E).
The number of favorable arrangements is then 9!.
Therefore, the probability is given by:
P(favorable arrangements) = (number of favorable arrangements) / (total number of possible arrangements)
P(favorable arrangements) = 9! / 10!
Simplifying this expression, we get:
P(favorable arrangements) = 1/10
Therefore, the probability that the two R's are together in a random arrangement of the letters in the word "arrangement" is 1/10 or 0.1.
The word "arrangement" has 11 letters, but two of them are repeated (R). Therefore, we have a total of 10 distinct letters.
The total number of possible arrangements of these 10 letters is 10!.
Now, let's consider the favorable arrangements. We want to find the probability that the two R's are together (RR).
To calculate this, we can treat the two R's as a single letter. This reduces the problem to arranging 9 distinct letters (A, A, N, G, E, M, T, N, E).
The number of favorable arrangements is then 9!.
Therefore, the probability is given by:
P(favorable arrangements) = (number of favorable arrangements) / (total number of possible arrangements)
P(favorable arrangements) = 9! / 10!
Simplifying this expression, we get:
P(favorable arrangements) = 1/10
Therefore, the probability that the two R's are together in a random arrangement of the letters in the word "arrangement" is 1/10 or 0.1.
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