The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition, is

$$\sum\limits_{k = 0}^6 {{}^{51 - k}{C_3}} $$ is equal to

The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is

The number of ways to distribute 30 identical candies among four children C₁, C₂, C₃ and C₄ so that C₂ receives at least 4 and at most 7 candies, C₃ receives at least 2 and at most 6 candies, is equal to: