If $n = ^mC_2$,then the value of $^nC_2$ is given by

Assuming that the balls of the same color are identical,find the number of ways to select one or more balls from $10$ white,$9$ green,and $7$ black balls.

The number of numbers greater than $5000$ and less than $9000$ that are divisible by $3$, which can be formed using the digits $0, 1, 2, 5, 9$ with repetition allowed, is . . . . . . .

The number of $4$-digit integers in the closed interval $[2022, 4482]$ formed by using the digits $0, 2, 3, 4, 6, 7$ is:

The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is

The value of the expression ${ }^{47} C_4 + \sum_{j=1}^5 { }^{52-j} C_3$ is