Slide28.JPG

Slide29.JPG

Go Ad-free

Transcript

Example 12 Find the value of n such that (ii) "nP4" /"nāˆ’1P4" = 5/3 , n > 4 Lets first calculate nP4 and n ā€“ 1P4 nP4 = š‘›!/(š‘› āˆ’ 4)! = (š‘›(š‘› āˆ’ 1)(š‘› āˆ’ 2)(š‘› āˆ’ 3)(š‘› āˆ’ 4)!)/(š‘› āˆ’ 4)! = n(n ā€“ 1)(n ā€“ 2)(n ā€“ 3) n ā€“ 1P4 = ((š‘› āˆ’ 1)!)/(š‘› āˆ’ 1 āˆ’ 4)! = ((š‘› āˆ’ 1)!)/(š‘› āˆ’ 5)! = ((š‘› āˆ’ 1)(š‘› āˆ’ 2)(š‘› āˆ’ 3)(š‘› āˆ’ 4)(š‘› āˆ’ 5)!)/(š‘› āˆ’ 5)! = (n ā€“ 1) (n ā€“ 2) (n ā€“ 3) (n ā€“ 4) nPr = ((š‘›)!)/(š‘› āˆ’ š‘Ÿ)! Now "nP4" /"nāˆ’1P4" = 5/3 3 nP4 = 5 n-1P4 3(n)(n ā€“ 1)(n ā€“ 2)(n ā€“ 3) = 5(n ā€“ 1) (n ā€“ 2) (n ā€“ 3) (n ā€“ 4) (3š‘›(š‘› āˆ’1)(š‘› āˆ’2)(š‘› āˆ’ 3))/((š‘› āˆ’1)(š‘› āˆ’2)(š‘› āˆ’ 3)) = 5(n ā€“ 4) 3n = 5(n ā€“ 4) 3n = 5n ā€“ 20 20 = 5n ā€“ 3n 20 = 2n 20/2 = n 10 = n Hence, n = 10 n(n ā€“ 10) + 3(n ā€“ 10) = 0 (n ā€“ 10) (n + 3) = 0 So, n = 10, and n = ā€“3 But, It is given in question n > 4 So n = ā€“3 not possible Therefore, n = 10 only Example 12 Find the value of n such that (ii) "nP4" /"nāˆ’1P4" = 5/3 , n > 4 Lets first calculate nP4 and n ā€“ 1P4 nP4 = š‘›!/(š‘› āˆ’ 4)! = (š‘›(š‘› āˆ’ 1)(š‘› āˆ’ 2)(š‘› āˆ’ 3)(š‘› āˆ’ 4)!)/(š‘› āˆ’ 4)! = n(n ā€“ 1)(n ā€“ 2)(n ā€“ 3) n ā€“ 1P4 = ((š‘› āˆ’ 1)!)/(š‘› āˆ’ 1 āˆ’ 4)! = ((š‘› āˆ’ 1)!)/(š‘› āˆ’ 5)! = ((š‘› āˆ’ 1)(š‘› āˆ’ 2)(š‘› āˆ’ 3)(š‘› āˆ’ 4)(š‘› āˆ’ 5)!)/(š‘› āˆ’ 5)! = (n ā€“ 1) (n ā€“ 2) (n ā€“ 3) (n ā€“ 4) nPr = ((š‘›)!)/(š‘› āˆ’ š‘Ÿ)! Now "nP4" /"nāˆ’1P4" = 5/3 3 nP4 = 5 n-1P4 3(n)(n ā€“ 1)(n ā€“ 2)(n ā€“ 3) = 5(n ā€“ 1) (n ā€“ 2) (n ā€“ 3) (n ā€“ 4) (3š‘›(š‘› āˆ’1)(š‘› āˆ’2)(š‘› āˆ’ 3))/((š‘› āˆ’1)(š‘› āˆ’2)(š‘› āˆ’ 3)) = 5(n ā€“ 4) 3n = 5(n ā€“ 4) 3n = 5n ā€“ 20 20 = 5n ā€“ 3n 20 = 2n 20/2 = n 10 = n Hence, n = 10

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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo