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 ๐‘›!/9!(๐‘›โˆ’9)! = ๐‘›!/(๐‘›โˆ’8)!8! ๐‘›!(๐‘›โˆ’8)!/(๐‘›โˆ’9)!๐‘›! = (9! )/8! (๐‘›โˆ’8)!/((๐‘›โˆ’9)! ) = (9! )/8! ((๐‘›โˆ’8)(๐‘› โˆ’8 โˆ’1)!)/((๐‘›โˆ’9)! ) = (9 ร— 8! )/8! ((๐‘›โˆ’8)(๐‘› โˆ’9)!)/((๐‘›โˆ’9)! ) = 9 n โ€“ 8 = 9 n = 17 Now we have to find nC17 Putting n = 17 = 17C17 = 17!/17!(17 โˆ’17)! = 17!/(17! ร— 0!) = 17!/(17!ร—1) = 1/1 = 1

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