**Concept: The question tests on the application of Combinatorics in a DS format**

**Solution:**

These apple are distinguishable, i.e. distinct

The number of ways

(i) 4 3 1. This can be done in 8C4 * 4C3 * 1C1 = 70 * 4 * 1 = 280 and which can be arranged in 3! = 6 ways.

Total ways = 280 * 6 = 1680

(ii) 4 2 2. This can be done in 8C4 * 4C2 * 2C2 = 70 * 6 * 1 = 420 and which can be arranged in 3!/2! = 3 ways

Total Ways = 420 * 3 = 1260

(iii) 3 3 2. This can be done in 8C3 * 5C3 * 2C2 = 56 * 10 * 1 = 560 and which can be arranged in 3!/2! = 3 ways

Total ways = 560 * 3 = 1680

The total number of ways = (1680 + 1260 + 1680) = 4620

K * 7P3 = K * 7!/(7 - 3)! = K * 7 * 6 * 5 = 210K

210K = 4620

K = 22**Option D**