For 1 ≤ r ≤ n ,   1 r + 1 P r + 1 n - P r + 1 ( n - 1 ) is equal to

For 1≤r≤n, 1r+1Pr+1n-Pr+1(n-1) is equal to
  1. nPn
  2. n−1Pr
  3. nPn+1
  4. 0

Solution

Using Prn=n!n-r! we get,

1r+1Pr+1n-Pr+1(n-1)=1r+1n!n-r-1!-n-1!n-r-1-1!

=1r+1n!-n-r-1n-1!n-r-1!

=1r+1n-1!n-n+r+1n-r-1!

=n-1!n-r-1!

=Prn-1

Asked in: AP EAMCET 2021 (19 Aug Shift 2)

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