Mr. $A$ has six children and atleast one child is a girl, then probability that Mr. $A$ has $3$ boys and $3$ girls, is -
 

If a party of $n$ persons sit at a round table, then the odds against two specified individuals sitting next to each other are

A lot consists of $12$ good pencils, $6$ with minor defects and $2$ with major defects. A pencil is choosen at random. The probability that this pencil is not defective is

The letter of the word `$ASSASSIN$' are written down at random in a row. The probability that no two $S$ occur together 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

A box $'A'$ contanis $2$ white, $3$ red and $2$ black balls. Another box $'B'$ contains $4$ white, $2$ red and $3$ black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box $'B'$ is