There are $6$ multiple choice questions in an examination. How many sequences of answers are possible,if the first three questions have $4$ choices each and the next three have $5$ choices each?

Three horses $H_{1}, H_{2}, H_{3}$ entered a field which has $7$ portions marked $P_{1}, P_{2}, P_{3}, P_{4}, P_{5}, P_{6}$ and $P_{7}$. If no $2$ horses are allowed to enter the same portion of the field,in how many ways can the horses graze the grass of the field?

How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if each digit appears not more than once in each number?

How many words,each of $3$ vowels and $2$ consonants,can be formed from the letters of the word '$INVOLUTE$'?

In how many ways can $6$ apples be distributed among $3$ boys,there being no restriction to the number of apples each boy may get?

The number of different words that can be formed from the letters of the word $SUCCESS$ in which the two $C$ are together but no two $S$ are together are: