The total number of different combinations of one or more letters which can be made from the letters of the word '$MISSISSIPPI$' is

All possible numbers are formed using the digits $1, 1, 2, 2, 2, 2, 3, 4, 4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is

In the given figure,$6$ '$A$'s should be written in such a manner that every row contains at least one '$A$'. The number of ways this is possible is:

If the permutations of $A, B, C, D, E$ taken all together are written down in alphabetical order as in a dictionary and numbered,then the rank of the permutation $DEBAC$ is

The set $S = \{1, 2, 3, \ldots, 12\}$ is to be partitioned into three sets $A, B, C$ of equal size. Thus $A \cup B \cup C = S$ and $A \cap B = B \cap C = C \cap A = \emptyset$. The number of ways to partition $S$ is

$A$ group of students comprises $5$ boys and $n$ girls. If the number of ways in which a team of $3$ students can be selected from this group such that there is at least one boy and at least one girl in each team is $1750$,then $n$ is equal to: