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How many words can be formed by re-arranging the letters of the word P
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28 Sep 2021, 09:27
28 Sep 2021, 09:27
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Question Stats:
80% (00:56) correct
19% (01:19) wrong based on 26 sessions
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How many words can be formed by re-arranging the letters of the word PROBLEMS such that P and S occupy the first and last position respectively? (Note: The words thus formed need not be meaningful)
A. 8/2
B. 6!
C. 6! * 2!
D. 8! - 2*7!
E. 8! - 2!
A. 8/2
B. 6!
C. 6! * 2!
D. 8! - 2*7!
E. 8! - 2!
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How many words can be formed by re-arranging the letters of the word P
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28 Sep 2021, 09:44
28 Sep 2021, 09:44
1
Carcass wrote:
How many words can be formed by re-arranging the letters of the word PROBLEMS such that P and S occupy the first and last position respectively? (Note: The words thus formed need not be meaningful)
A. 8/2
B. 6!
C. 6! * 2!
D. 8! - 2*7!
E. 8! - 2!
A. 8/2
B. 6!
C. 6! * 2!
D. 8! - 2*7!
E. 8! - 2!
Take the task of arranging the 8 letters and break it into stages.
Begin with the most restrictive stages.
Stage 1: Select a letter for the 1st position
Since the first letter must be P, we can complete stage 1 in 1 way
Stage 2: Select a letter for the last (8th) position
Since the last letter must be S, we can complete stage 2 in 1 way
Stage 3: Select a letter for the 2nd position
There are 6 remaining letters from which to choose
So, we can complete stage 3 in 6 ways
Stage 4: Select a letter for the 3rd position
There are 5 remaining letters from which to choose
So, we can complete stage 4 in 5 ways
Stage 5: Select a letter for the 4th position
4 letters remaining. So, we can complete stage 5 in 4 ways
Stage 6: Select a letter for the 5th position
3 letters remaining. So, we can complete stage 6 in 3 ways
Stage 7: Select a letter for the 6th position
2 letters remaining. So, we can complete stage 7 in 2 way
Stage 8: Select a letter for the 7th position
1 letter remaining. So, we can complete stage 8 in 1 way
By the Fundamental Counting Principle (FCP), we can complete all 8 stages (and thus seat all 6 children) in (1)(1)(6)(5)(4)(3)(2)(1) ways (= 6! ways)
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
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Re: How many words can be formed by re-arranging the letters of the word P
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28 Sep 2021, 09:38
28 Sep 2021, 09:38
Carcass wrote:
How many words can be formed by re-arranging the letters of the word PROBLEMS such that P and S occupy the first and last position respectively? (Note: The words thus formed need not be meaningful)
A. 8/2
B. 6!
C. 6! * 2!
D. 8! - 2*7!
E. 8! - 2!
A. 8/2
B. 6!
C. 6! * 2!
D. 8! - 2*7!
E. 8! - 2!
since P and S will be the first and last, the only changing letters are ROBLEM, so 6 letters and 6 positions.
Answer is 6!.
