Five digit numbers are formed using the digits $1, 2, 3, 4, 5, 6$ and $8$. What is the probability that they have even digits at both the ends

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

A box contains $24$ identical balls, of which $12$ are white and $12$ are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw is

Out of $100$ students, two sections of $40$ and $60$ are formed. If you and your friend are among the $100$ students, what is the probability that you both enter the same section ?

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

A mapping is selected at random from the set of all the mappings of the set $A = \left\{ {1,\,\,2,\,...,\,n} \right\}$ into itself. The probability that the mapping selected is an injection is