Compute $\frac{12!}{10! \times 2!}$

Given $5$ different green toys,$4$ different blue toys,and $3$ different red toys,how many combinations of toys can be chosen taking at least one green and one blue toy?

$A$ die is rolled three times. Find the probability of getting a larger number than the previous number each time.

$A$ linguistic club of a certain Institute consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this group,including the selection of a Captain (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:

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

Six '$+$' and four '$-$' signs are to be placed in a straight line so that no two '$-$' signs come together. Then the total number of ways is: