If `""^(n)P_r: ""^(n)C_(r)=120` find the value of r

If ""^(n)P_(r) = ""^(n)P_(r+1) and ""^(n)C_(r) = ""^(n) C_(r-1) then the value of r is equal to

If ^(n+1)C_(r+1): ^nC_r: ^(n-1)C_(r-1)=11:6:2 find the values of n and r.

If ""^(n)C_(r )""^(r )C_(5)=""^(n)C_(5) ""^(n+s)C_(r+s) find the value of s .

If ""^(n)P_r = ""^(n)P_(r+1) and ""^(n)C_r = ""^(n)C_(r-1) ,then the values of n and r are

If .^(n)C_(r-1): .^(n)C_(r): .^(n)C_(r+1)=3:4:5 , find the values of n and r.

If .^(n)P_(r)=720 and .^(n)C_(r)=120 then find the value of r.

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))

If .^(n+1)C_(r+1):^(n)C_(r):^(n-1)C_(r-1)=11:6:3 , find the values of n and r.

If ""^(n)C_(r -1) = 36, ""^(n)C_(r) = 84 " and " ""^(n)C_(r +1) = 126 , then find the value of ""^(r)C_(2) .