How many distinct words can be formed using the letters of the word $EQUATION$ such that the word starts and ends with a consonant?

The number of integers between $2,000$ and $5,000$ that can be formed using the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) such that the number is a multiple of $3$ is:

If ${}^{27}P_{r+7} = 7722 \times {}^{25}P_{r+4}$,then $r = $

The numbers $1, 2, 3,$ and $4$ are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. $A$ person draws two slips from the box,one after the other,without replacement. Describe the sample space for the experiment.

Using the digits $0, 2, 4, 6, 8$ not more than once in any number,the number of $5$-digit numbers that can be formed is:

Evaluate $5!$