Last updated at Jan. 30, 2020 by Teachoo
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Example 17 (Method 1) If nC9 = nC8, find nC17 . nC9 = nC8 ๐!/9!(๐ โ 9)! = ๐!/(๐ โ 8)!8! ๐!(๐ โ 8)!/(๐ โ 9)!๐! = (9! )/8! (๐ โ 8)!/((๐ โ 9)! ) = (9! )/8! ((๐ โ 8)(๐ โ 8 โ 1)!)/((๐ โ 9)! ) = (9 ร 8! )/8! ((๐ โ 8)(๐ โ 9)!)/((๐ โ 9)! ) = 9 n โ 8 = 9 n = 17 nCr = ๐!/๐!(๐ โ ๐)! Now we have to find nC17 Putting n = 17 = 17C17 = 17!/17!(17 โ 17)! = 17!/(17! ร 0!) = 17!/(17! ร 1) = 1/1 = 1 Example, 17 (Alternative Method) If nC9 = nC8, find nC17 . Given nC9 = 4C8 If nCp = nCq then either p = q or p + q = n p = q 9 = 8 Which is not possible p + q = n 9 + 8 = n n = 17 Now we have to find nC17 Putting n = 17 = 17C17 = 17!/17!(17 โ 17)! = 17!/(17! ร 0!) = 17!/(17! ร 1) = 1/1 = 1
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