if 10Pr+ 1:11 Pr =30:11 find r
Answer :
We have : 10 P r + 1 : 11 P r = 30 : 11
We get
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( 11 - r ) ( 10 - r ) = 30
110 - 11 r - 10 r + r2 = 30
r2 - 21r + 80 = 0
Using splitting the middle term method and get
r2 - 16 r - 5r + 80 = 0
r ( r - 16 ) - 5 ( r - 16 ) = 0
( r - 16 ) ( r - 5 ) = 0
So,
r = 5 , 16
But r cannot be 16 as r lies between 0 and n and here n = 10 or 11.
SO,
r = 5 ( Ans )
We have : 10 P r + 1 : 11 P r = 30 : 11
We get
=
=
=
=
( 11 - r ) ( 10 - r ) = 30
110 - 11 r - 10 r + r2 = 30
r2 - 21r + 80 = 0
Using splitting the middle term method and get
r2 - 16 r - 5r + 80 = 0
r ( r - 16 ) - 5 ( r - 16 ) = 0
( r - 16 ) ( r - 5 ) = 0
So,
r = 5 , 16
But r cannot be 16 as r lies between 0 and n and here n = 10 or 11.
SO,
r = 5 ( Ans )