Question:
if a denotes the number of permutations of x 2 things taken all at a time , b the number of permetation of x thing taken 11 at a time and c the number of permetations of x-11 things taken all at a time such that a=182bc then the value of x is
Answer:
Given that a denotes the number of permutations of (x+2) things taken all at a time
=> a = x+2Px+2 = (x+2)! (Since nPn = n!/(n-n)! = n!/0! = n!, 0! = 1)
b denotes the number of permutation of x thing taken 11 at a time
=> b = xP11 = x!/(x-11)!
c denotes the number of permetations of (x-11) things taken all at a time
=> c = x-11Px-11 = (x - 11)!
Given that
a = 182bc
Put value of a,b and c, we get
(x+2)! = 182* x!/(x-11)! * (x- 11)!
=> (x+2)*(x+1)*x! = 182*x!
=> (x+2)*(x+1) = 182
=> x2 + 3x + 2 = 182
=> x2 + 3x + 2 - 182 = 0
=> x22 + 3x - 180 = 0
=> (x-12)*(x+15) = 0
=> x = 12, -15
So value of x = 12, -15
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