There are $6$ men and $8$ women in a club. $A$ committee of $5$ people has to be formed. What will be the number of ways to select $5$ people if $2$ men and $3$ women are selected?

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?

$A$ number lock consists of three rings. If the $1^{st}$ ring is marked with digits $0$ to $9$,the $2^{nd}$ ring is marked with prime numbers greater than $2$ but less than $30$,and the $3^{rd}$ ring is marked with all vowels,find the total number of unsuccessful attempts.

There are $4$ parcels and $5$ post-offices. In how many different ways can the registration of the parcels be made?

The number of arrangements of the letters of the word $BANANA$ in which two $N$s do not appear adjacently is

$n$ balls each of weight $w$ are weighed in pairs. The sum of the weights of all possible pairs is $120$. When they are weighed in triplets,the sum of the weights of all possible triplets is $480$. Then $n$ is: