If the letters of the word $COCHIN$ are rearranged and all permutations are arranged in alphabetical order as in an English dictionary,how many words appear before the word $COCHIN$?

Six objects $O_1$ to $O_6$ are arranged one on top of the other. In how many ways can these be arranged such that $O_1$ and $O_2$ are the $2$ bottom-most objects?

If the number of words,with or without meaning,which can be made using all the letters of the word $MATHEMATICS$ in which $C$ and $S$ do not come together,is $(6 !) k$,then $k$ is equal to $............$.

Find the number of arrangements of the letters of the word $INDEPENDENCE$. In how many of these arrangements do the words start with $P$?

The number of $5$-letter words that can be formed by using the letters of the word $SARANAM$ is

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.