CA Foundation Exam > CA Foundation Questions > If . nP3 : nP2 = 3 : 1, then n is equal toa)7...
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If . nP3 : nP2 = 3 : 1, then n is equal to
- a)7
- b)4
- c)5
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If . nP3 : nP2 = 3 : 1, then n is equal toa)7b)4c)5d)none of theseCorr...
We are given the ratio of permutations nP3 : nP2 = 3 : 1, and we need to find the value of n.
First, recall the formula for permutations:
P(n, r) = n! / (n - r)!
P(n, r) = n! / (n - r)!
Using this formula, we can express the permutations:
nP3 = n! / (n - 3)! = n(n-1)(n-2)
nP2 = n! / (n - 2)! = n(n-1)
Now, we substitute these into the given ratio:
(n(n-1)(n-2)) / (n(n-1)) = 3 / 1
nP2 = n! / (n - 2)! = n(n-1)
Now, we substitute these into the given ratio:
(n(n-1)(n-2)) / (n(n-1)) = 3 / 1
On simplifying:
(n-2) = 3
(n-2) = 3
Solving for n:
n = 3 + 2 = 5
Therefore, the value of n is 5.
n = 3 + 2 = 5
Therefore, the value of n is 5.
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If . nP3 : nP2 = 3 : 1, then n is equal toa)7b)4c)5d)none of theseCorr...
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If . nP3 : nP2 = 3 : 1, then n is equal toa)7b)4c)5d)none of theseCorr...
Ratio of nP3 to nP2
The question states that the ratio of nP3 to nP2 is 3:1.
nP3 represents the number of permutations of n objects taken 3 at a time, which is given by n(n-1)(n-2).
nP2 represents the number of permutations of n objects taken 2 at a time, which is given by n(n-1).
So, we can write the given ratio as:
n(n-1)(n-2) : n(n-1) = 3:1
Simplifying the ratio
We can simplify the ratio by dividing both sides by n(n-1):
(n-2) : 1 = 3:1
Cross-multiplying, we get:
n-2 = 3
Solving for n:
n = 5
Therefore, the value of n is 5.
Answer: Option C
The question states that the ratio of nP3 to nP2 is 3:1.
nP3 represents the number of permutations of n objects taken 3 at a time, which is given by n(n-1)(n-2).
nP2 represents the number of permutations of n objects taken 2 at a time, which is given by n(n-1).
So, we can write the given ratio as:
n(n-1)(n-2) : n(n-1) = 3:1
Simplifying the ratio
We can simplify the ratio by dividing both sides by n(n-1):
(n-2) : 1 = 3:1
Cross-multiplying, we get:
n-2 = 3
Solving for n:
n = 5
Therefore, the value of n is 5.
Answer: Option C
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If . nP3 : nP2 = 3 : 1, then n is equal toa)7b)4c)5d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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If . nP3 : nP2 = 3 : 1, then n is equal toa)7b)4c)5d)none of theseCorrect answer is option 'C'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If . nP3 : nP2 = 3 : 1, then n is equal toa)7b)4c)5d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If . nP3 : nP2 = 3 : 1, then n is equal toa)7b)4c)5d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
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