If nP3 + nCn-2 = 14n, then the value of n is
5
6
8
10
Step(i) :- General Formula of prn
prn=n!(n-r)!
Step(ii) :- Explanation
p3n+Cn-2n=14n
n!(n-3)!+n!(n-2)!×2!=14nn(n-1)(n-2)+n(n-1)2=14nn(n-1)n-2+12=14nn(n-1)(2n-3)=28n(n-1)(2n-3)=282n2-5n-25=0(n-5)(2n+5)=0n=5or-52
As n cannot be negative.
Hence, the value of n is 5.
Hence, Option (a) is the correct answer
If nP3+nCn−2 = 14n, then n =