Find n if `""^(n-1)P_(3) : ""^(n)P_(4) = 1:16`.

Find n if "^(n-1)P_3 : "^nP_4 =1:9 .

Find n, if ""^(2n)C_(1),""^(2n)C_(2) and ""^(2n)C_(3) are in A.P.

Find n if : "^(2n)P_3=100 ^nP_2 .

Find n if : 2^5P_3= "^nP_4 .

Prove that 1+1* ""^(1)P_(1)+2* ""^(2)P_(2)+3* ""^(3)P_(3) + … +n* ""^(n)P_(n)=""^(n+1)P_(n+1).

Prove that : ^nP_r= "^(n-1)P_r+r ^(n-1)P_(r-1) , for all natural numbers n and r for which the symbols are defined.

If .^(2n+1)P_(n-1):^(2n-1)P_(n)=7:10 , then .^(n)P_(3) equals

Consider a polygon of sides 'n' which satisfies the equation 3*^(n)P_(4)=^(n-1)P_(5) . Q. Number of quadrilaterals thatn can be formed using the vertices of a polygon of sides 'n' if exactly 1 side of the quadrilateral in common with side of the n-gon, is

If .^(m+n) P_(2)=56 and .^(m-n)P_(3)=24 , then (.^(m)P_(3))/(.^(n)P_(2)) equals