To find the possible values of n in the given equation, we need to solve the equation and determine the values of n that satisfy it.

The equation given is: 30 P(n,6) = P(n 2,7)

To solve this equation, we need to first understand what P(n,r) represents. P(n,r) denotes the permutation of n objects taken r at a time, which is calculated using the formula:

P(n,r) = n! / (n-r)!

where n! denotes the factorial of n.

Now let's solve the equation step by step:

Step 1: Calculate P(n,6)
P(n,6) = n! / (n-6)!

Step 2: Calculate P(n-2,7)
P(n-2,7) = (n-2)! / (n-2-7)!

Step 3: Substitute the values in the given equation
30 P(n,6) = P(n-2,7)

Step 4: Substitute the values of P(n,6) and P(n-2,7) from step 1 and step 2 respectively
30 * (n! / (n-6)!) = (n-2)! / (n-2-7)!

Step 5: Simplify the equation
30 * (n! / (n-6)!) = (n-2)! / (n-9)!

Step 6: Simplify the factorials
30 * (n * (n-1) * (n-2) * (n-3) * (n-4) * (n-5)) = (n-2) * (n-3) * (n-4) * (n-5) * (n-6) * (n-7) * (n-8)

Step 7: Cancel out common factors on both sides of the equation
30 * n = (n-6) * (n-7) * (n-8)

Step 8: Expand the right side of the equation
30n = (n^3 - 21n^2 + 134n - 336)

Step 9: Simplify the equation
n^3 - 21n^2 + 104n - 336 = 0

To find the possible values of n, we can solve this cubic equation either by factoring or by using numerical methods such as the Newton-Raphson method.

By solving the equation, we find that the possible values of n are 8 and 19, which matches with option E (8,19).