It is required to seat $5$ men and $4$ women in a row so that the men occupy odd places. Then the number of arrangements that are possible is

Find the sample space associated with the experiment of rolling a pair of dice (one is blue and the other red) once. Also,find the number of elements of this sample space.

How many arrangements can be made with $5$ boys and $5$ girls in a row such that boys and girls alternate?

If all permutations of the letters of the word $MASK$ are arranged in the order as in a dictionary,with or without meaning,which one of the following is the $19^{th}$ word?

There are $6$ letters and $3$ post boxes. In how many ways can these letters be posted in the post boxes?

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.