Example 17 - If nC9  = nC8, find nC17 - Chapter 7 - Combination formula

  1. Chapter 7 Class 11 Permutations and Combinations
  2. Serial order wise
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Example, 17 If nC9 = nC8, find nC17 . nC9 = nC8 !/9!( 9)! = !/( 8)!8! !( 8)!/( 9)! ! = (9! )/8! ( 8)!/(( 9)! ) = (9! )/8! (( 8)( 8 1)!)/(( 9)! ) = (9 8! )/8! (( 8)( 9)!)/(( 9)! ) = 9 n 8 = 9 n = 17 Now we have to find nC17 Putting n = 17 = 17C17 = 17!/17!(17 17)! = 17!/(17! 0!) = 17!/(17! 1) = 1/1 = 1

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