The product of $r$ consecutive natural numbers is always divisible by......

The number of ways in which an examiner can assign $30$ marks to $8$ questions,giving not less than $2$ marks to any question,is

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn,two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

$A$ committee of $5$ is to be formed out of $6$ men and $4$ ladies. The number of ways this can be done,when at most $2$ ladies are included,is

$A$ student has to answer $10$ out of $13$ questions in an examination,choosing at least $5$ questions from the first $6$ questions. The number of choices available to the student is:

$A$ committee of $12$ is to be formed from $9$ women and $8$ men such that at least $5$ women are included. Find the number of committees in which women are in the majority and the number of committees in which men are in the majority,respectively.