How many words of $4$ letters beginning with '$A$' or '$E$' can be formed with the letters of the word '$EQUATOR$'?

The number of ways in which $9$ persons can be divided into three equal groups is

The number of four-digit numbers strictly greater than $4321$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ (repetition of digits is allowed) is

If $\sum_{i=0}^4 {^{4+i}}C_i + \sum_{j=6}^9 {^{3+j}}C_j = {^x}C_y$ ($x$ is a prime number),then which one of the following is incorrect?

If all the words (with or without meaning) having five letters,formed using the letters of the word $SMALL$ and arranged as in a dictionary,then the position of the word $SMALL$ is:

$A$ box contains two white balls,three black balls,and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?