Check sibling questions

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

Example 17 - Chapter 7 Class 11 Permutations and Combinations - Part 2
Example 17 - Chapter 7 Class 11 Permutations and Combinations - Part 3
Example 17 - Chapter 7 Class 11 Permutations and Combinations - Part 4

This video is only available for Teachoo black users


Transcript

Example 17 (Method 1) If nC9 = nC8, find nC17 . nC9 = nC8 𝑛!/9!(𝑛 βˆ’ 9)! = 𝑛!/(𝑛 βˆ’ 8)!8! 𝑛!(𝑛 βˆ’ 8)!/(𝑛 βˆ’ 9)!𝑛! = (9! )/8! (𝑛 βˆ’ 8)!/((𝑛 βˆ’ 9)! ) = (9! )/8! ((𝑛 βˆ’ 8)(𝑛 βˆ’ 8 βˆ’ 1)!)/((𝑛 βˆ’ 9)! ) = (9 Γ— 8! )/8! ((𝑛 βˆ’ 8)(𝑛 βˆ’ 9)!)/((𝑛 βˆ’ 9)! ) = 9 n – 8 = 9 n = 17 nCr = 𝑛!/π‘Ÿ!(𝑛 βˆ’ π‘Ÿ)! Now we have to find nC17 Putting n = 17 = 17C17 = 17!/17!(17 βˆ’ 17)! = 17!/(17! Γ— 0!) = 17!/(17! Γ— 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 βˆ’ 17)! = 17!/(17! Γ— 0!) = 17!/(17! Γ— 1) = 1/1 = 1

Davneet Singh's photo - Teacher, Engineer, Marketer

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.