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CA Foundation Exam  >  CA Foundation Questions  >  m+nP2 = 56, m–nP2 = 30 thena)m =6, n = ... Start Learning for Free
m+nP2 = 56, m–nP2 = 30 then
  • a)
    m =6, n = 2
  • b)
    m = 7, n= 1
  • c)
    m=4,n=4
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
m+nP2 = 56, m–nP2 = 30 thena)m =6, n = 2b)m = 7, n= 1c)m=4,n=4d)...
We are given the following two permutation equations:
m+nP2 = 56
m–nP2 = 30
First, recall the formula for permutations:
    P(n, r) = n! / (n - r)!
    
For P2, this simplifies to:
    P(n, 2) = n(n-1)
    
Now, let's substitute the given values into the permutation formula:
m+nP2 = (m+n)(m+n-1) = 56
m–nP2 = (m-n)(m-n-1) = 30
We now have the system of equations:
    (m+n)(m+n-1) = 56
    
    (m-n)(m-n-1) = 30
    
Let's solve each equation:
1. Solve for m + n:
    (m+n)(m+n-1) = 56
    (m+n)(m+n-1) = 56
    m+n = 8 (since 8×7 = 56)
    
2. Solve for m - n:
    (m-n)(m-n-1) = 30
    (m-n)(m-n-1) = 30
    m-n = 6 (since 6×5 = 30)
    
Now, we have:
    m + n = 8
    m - n = 6
    
Adding these two equations:
    (m+n) + (m-n) = 8 + 6
    2m = 14
    m = 7
    
Substituting m = 7 into m + n = 8:
    7 + n = 8
    n = 1
    
Therefore, m = 7 and n = 1.
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Most Upvoted Answer
m+nP2 = 56, m–nP2 = 30 thena)m =6, n = 2b)m = 7, n= 1c)m=4,n=4d)...
m = 8 
and hence n = 10−m = 2 
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Community Answer
m+nP2 = 56, m–nP2 = 30 thena)m =6, n = 2b)m = 7, n= 1c)m=4,n=4d)...
Given:

m nP2 = 56

mnP2 = 30

We need to find the values of m and n.

Solution:

nP2 means selecting 2 items from n items, where order matters.

m nP2 = 56

This means selecting 2 items from m items, where order matters, gives 56 different possibilities.

To find the value of m, we can use trial and error method.

Let us start with m = 8, then we get:

8P2 = 8x7 = 56

So, m = 8 is a valid solution.

Now, let us find the value of n using the second equation.

mnP2 = 30

Substitute m = 8, we get:

8nP2 = 30

nP2 = 30/8 = 3.75

This is not possible as nP2 should be a whole number.

Let us try with m = 7, then we get:

7P2 = 7x6 = 42

So, m = 7 is a valid solution.

Substitute m = 7 in the second equation, we get:

7nP2 = 30

nP2 = 30/7

This is not possible as nP2 should be a whole number.

Let us try with m = 6, then we get:

6P2 = 6x5 = 30

So, m = 6 is a valid solution.

Substitute m = 6 in the first equation, we get:

6nP2 = 56

nP2 = 56/6 = 9.33

This is not possible as nP2 should be a whole number.

Therefore, the only valid solution is m = 7 and n = 1.

Hence, the correct answer is option B) m = 7, n = 1.
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m+nP2 = 56, m–nP2 = 30 thena)m =6, n = 2b)m = 7, n= 1c)m=4,n=4d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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