How many words can be formed from the letters of the word $COURTESY$,whose first letter is $C$ and the last letter is $Y$?

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:

The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball,is

Choose the correct number of ways in which $15$ different books can be divided into five heaps of equal number of books.

How many arrangements can be made of the letters of the word '$ARRANGEMENT$'?

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