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04 Mar 2021, 09:30
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:21) correct
39%
(02:25)
wrong
based on 274
sessions
History
Date
Time
Result
Not Attempted Yet
The letters of the word PROMISE are arranged. One of the arrangements is then picked at random. What is the probability that there are 3 letters between P and R in that arrangement?
A. 2/7
B. 1/5
C. 1/6
D. 1/7
E. 1/14
A. 2/7
B. 1/5
C. 1/6
D. 1/7
E. 1/14
04 Mar 2021, 18:04
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Probability = Favorable Outcomes / Total Outcomes
PROMISE has 7 distinct letters
Favorable Outcomes = Having 3 letters between P and R. P and R can arrange themselves in 2 ways.
there are 3 ways of arranging P and R with 3 letters between them. P _ _ _ R _ _ or _ P _ _ _ R _ or _ _ P _ _ _ R
The remaining 5 letters can be arranged in 5! = 120 ways.
Total Favorable Outcomes = 2 * 3 * 120 = 720
Tot number of outcomes = Arranging all 7 letters = 7! = 5040
Required Probability = 720/5040 = 1/7
Option D
Arun Kumar
PROMISE has 7 distinct letters
Favorable Outcomes = Having 3 letters between P and R. P and R can arrange themselves in 2 ways.
there are 3 ways of arranging P and R with 3 letters between them. P _ _ _ R _ _ or _ P _ _ _ R _ or _ _ P _ _ _ R
The remaining 5 letters can be arranged in 5! = 120 ways.
Total Favorable Outcomes = 2 * 3 * 120 = 720
Tot number of outcomes = Arranging all 7 letters = 7! = 5040
Required Probability = 720/5040 = 1/7
Option D
Arun Kumar
30 Aug 2024, 09:19
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There are total 7 spaces
P and R are fixed others can be arranged in 5! ways
but P and R can be interchanged so we have total no of ways = 2 x 5!
now again P and R or R and P can be placed only at 3 places
P - - - R - - OR - P - - - R - OR - - P - - - R
So total no of ways = 3 x 2 x 5!
but total 7 distinct letters can be arranged in 7! ways in spaces
probability = 6 x 5! / 7! = 1/7
P and R are fixed others can be arranged in 5! ways
but P and R can be interchanged so we have total no of ways = 2 x 5!
now again P and R or R and P can be placed only at 3 places
P - - - R - - OR - P - - - R - OR - - P - - - R
So total no of ways = 3 x 2 x 5!
but total 7 distinct letters can be arranged in 7! ways in spaces
probability = 6 x 5! / 7! = 1/7
