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 $6$ black balls. If two balls are drawn at random, then the probability that one of them is white is

A bag contains $5$ brown and $4$ white socks. A man pulls out two socks. The probability that these are of the same colour is

A man draws a card from a pack of $52$ playing cards, replaces it and shuffles the pack. He continues this processes until he gets a card of spade. The probability that he will fail the first two times is

A bag contains $6$ white, $7$ red and $5$ black balls. If $3$ balls are drawn from the bag at random, then the probability that all of them are white is

A word consists of $11$ letters in which there are $7$ consonants and $4$ vowels. If $2$ letters are chosen at random, then the probability that all of them are consonants, is