The number of $3 \times 3$ matrices $A$ whose entries are either $0$ or $1$ and for which the system $\mathrm{A}\left[\begin{array}{l}\mathrm{x} \\ \mathrm{y} \\ \mathrm{z}\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has exactly two distinct solutions, is

A bag contains $4$ white, $5$ red and $6$ green balls. Three balls are picked up randomly. The probability that a white, a red and a green ball is drawn is

A committee consists of $9$ experts taken from three institutions $A, B$ and $C$, of which $2$ are from $A, 3$ from $B$ and $4$ from $C$. If three experts resign, then the probability that they belong to different institutions is

In a lottery there were $90$ tickets numbered $1$ to $90$. Five tickets were drawn at random. The probability that two of the tickets drawn numbers $15$ and $89$ is

Three vertices are chosen randomly from the seven vertices of a regular $7$ -sided polygon. The probability that they form the vertices of an isosceles triangle is

A committee of two persons is selected from two men and two women. What is the probability that the committee will have no man ?