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What is the value of  for m < n, m = n, m > n?

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  1. 0, n!, mPn x(m-n)
  2. mPn x(m-n), n!, 0
  3. 0, n!, mCn x(m-n)
  4. mCn x(m-n), n!, 0

Answer (Detailed Solution Below)

Option 1 : 0, n!, mPn x(m-n)

Detailed Solution

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Explanation:

 = ? ; for m < n, m = n, and m > n

∵  = 

Case: I

Since m > n, hence the cycle will move up to (m - n) times, and at last

 = 

Hence, for m > n,

 = mPn x(m - n)........................................................(1)

Case: II

For m = n:

From equation (1),

 = nPn x(n - n) =  n!

Case: III

For m < n:

 = mPn x(m - n) = 0 ( Because mPn = 0; For m < n )

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