The number of ways in which $n$ distinct objects can be put into two different boxes is

The number of ways to form a $7$-digit number using the digits $1, 2, 3, 4, 3, 2, 1$ such that odd digits always occupy odd places is:

If all the letters of the word $MOST$ are permuted and the words (with or without meaning) thus obtained are arranged in the dictionary order,then the rank of the word $STOM$ when counted from the rank of the word $MOST$ is:

How many ways are there to arrange the letters of the word $EDUCATION$ so that all the following three conditions hold?
- The vowels occur in the same order $(E, U, A, I, O)$.
- The consonants occur in the same order $(D, C, T, N)$.
- No two consonants are next to each other.

The number of arrangements of the letters of the word $ARRANGEMENT$ in which two $E$s do not occur adjacently is

In how many of the distinct permutations of the letters in $MISSISSIPPI$ do the four $I$'s not come together?