There are $6$ men and $8$ women in a club in which a committee of $5$ people has to be formed. What will be the number of ways to select $5$ people if no man is selected?

Each of the $10$ letters $A, H, I, M, O, T, U, V, W$ and $X$ appears the same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

$A$ number lock on a suitcase has $3$ wheels,each labelled with $10$ digits from $0$ to $9$. If opening the lock requires a particular sequence of $3$ digits with no repeats,how many such sequences are possible?

From $6$ different novels and $3$ different dictionaries,$4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

If ${ }^{18} C_{r}={ }^{18} C_{r+2}$,find ${ }^{r} C_{5}$.

Assuming the balls to be identical except for the difference in colours,the number of ways in which one or more balls can be selected from $10$ white,$9$ green,and $7$ black balls is: