The value of $\sum\limits_{r = 0}^{15} {\left( {{}^{15}{C_r} \cdot {}^{40}{C_{15}} \cdot {}^{20}{C_r} - {}^{35}{C_{15}} \cdot {}^{15}{C_r} \cdot {}^{25}{C_r}} \right)}$ is:

$A$ linguistic club consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this group including the selection of a leader (from among these $4$ members) for the team. If the team has to include at most one boy,the number of ways of selecting the team is

Total number of $3$ letter words that can be formed from the letters of the word $'SAHARANPUR'$ is equal to

$A$ building has a ground floor and $10$ more floors. Nine persons enter a lift at the ground floor. The lift goes up to the $10$th floor. The number of ways in which any $4$ persons exit at a floor and the remaining $5$ persons exit at a different floor,if the lift does not stop at the first and the second floors,is equal to:

There are $15$ stations on a train route and the train has to be stopped at exactly $5$ stations among these $15$ stations. If it stops at at least two consecutive stations,then the number of ways in which the train can be stopped is

An envelope has space for at most $3$ stamps. If you are given three stamps of denomination $1$ and three stamps of denomination $a$ (where $a > 1$),what is the least positive integer for which there is no possible stamp value?