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

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Example 17 (Method 1) If nC9 = nC8, find nC17 . nC9 = nC8 𝑛!/9!(𝑛 − 9)! = 𝑛!/(𝑛 − 8)!8! 𝑛!(𝑛 − 8)!/(𝑛 − 9)!𝑛! = (9! )/8! (𝑛 − 8)!/((𝑛 − 9)! ) = (9! )/8! ((𝑛 − 8)(𝑛 − 8 − 1)!)/((𝑛 − 9)! ) = (9 × 8! )/8! ((𝑛 − 8)(𝑛 − 9)!)/((𝑛 − 9)! ) = 9 n – 8 = 9 n = 17 nCr = 𝑛!/𝑟!(𝑛 − 𝑟)! Now we have to find nC17 Putting n = 17 = 17C17 = 17!/17!(17 − 17)! = 17!/(17! × 0!) = 17!/(17! × 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 − 17)! = 17!/(17! × 0!) = 17!/(17! × 1) = 1/1 = 1

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.