Question -
Answer -
Given:
n + 2C8:┬аn тАУ 2P4┬а=57: 16
n + 2C8┬а/┬аn тАУ 2P4┬а=57 / 16
Let us use theformula,
nCr┬а= n!/r!(n тАУ r)!
[(n+2)!(n-6)!] / [(n-6)! (n-2)! 8!] = 57/16
(n+2) (n+1) (n) (n-1)/ 8! = 57/16
(n+2) (n+1) (n) (n-1)= (57├Ч8!) / 16
(n+2) (n+1) (n) (n-1)= [19├Ч3 ├Ч 8├Ч7├Ч6├Ч5├Ч4├Ч3├Ч2├Ч1]/16
(n + 2) (n + 1) (n) (nтАУ 1) = 21 ├Ч 20 ├Ч 19 ├Ч 18
Equating thecorresponding terms on both sides we get,
n = 19
тИ┤┬аThe value of nis 19.