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

There are $3$ bags $A, B$ & $C$. Bag $A$ contains $1$ Red & $2$ Green balls, bag $B$ contains $2$ Red & $1$ Green balls and bag $C$ contains only one green ball. One ball is drawn from bag $A$ & put into bag $B$ then one ball is drawn from $B$ & put into bag $C$ & finally one ball is drawn from bag $C$ & put into bag $A$. When this operation is completed, probability that bag $A$ contains $2$ Red & $1$ Green balls, is -

Twenty tickets are marked the numbers $1, 2, ..... 20.$ If three tickets be drawn at random, then what is the probability that those marked $7$ and $11$ are among them

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text {th }}$ roll than the number obtained in the $(i-1)^{\text {th }}$ roll, $i=2,3$, is equal to :

If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is through five times, then the probability that the product of the outcomes is positive, is :

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, is equal to