In how many ways can $6$ '$+$' signs and $4$ '$*$' signs be arranged in a row such that no two '$*$' signs occur together?

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are two red cards and two black cards?

Out of $10$ white,$9$ black and $7$ red balls,the number of ways in which selection of one or more balls can be made,is

There are ten boys $B_{1}, B_{2}, \ldots, B_{10}$ and five girls $G_{1}, G_{2}, \ldots, G_{5}$ in a class. The number of ways of forming a group consisting of three boys and three girls,such that $B_{1}$ and $B_{2}$ are not both members of the same group,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:

How many words can be formed by taking $3$ consonants and $2$ vowels out of $5$ consonants and $4$ vowels?