If all the seven letters of the word $LEADING$ are permuted in all possible ways and the words thus formed are arranged as in the dictionary order,then the word in $2017^{\text{th}}$ place is

In how many ways can the letters of the word $TRIANGLE$ be arranged such that no two vowels occur together?

Seven scientists $S_1, S_2, \ldots, S_7$ are invited to deliver one lecture each in a conference. The number of ways all the seven lectures can be arranged such that the lecture of $S_1$ is prior to that of $S_3$ and the lecture of $S_3$ is prior to that of $S_7$ is

All words,with or without meaning,are made using all the letters of the word $MONDAY$. These words are written as in a dictionary with serial numbers. The serial number of the word $MONDAY$ is

In how many ways can one send $6$ new-year greeting cards to $4$ people?

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: