$A$ committee has to be made of $5$ members from $6$ men and $4$ women. The probability that at least one woman is present in the committee is:

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

$A$ bag contains $12$ two-rupee coins,$7$ one-rupee coins,and $4$ fifty-paise coins. If three coins are selected at random,the probability that the sum of the values of the three coins is not an integral multiple of a rupee is:

$A$ bag contains $6$ white and $4$ black balls. Two balls are drawn at random. The probability that they are of the same colour is . . . . . .

$A$ bag contains $5$ red balls, $3$ black balls, and $4$ white balls. Three balls are drawn at random. The probability that they are not of the same colour is

If each of the coefficients $a, b, c$ in the equation $ax^2 + bx + c = 0$ is determined by throwing a die,then the probability that the equation will have equal roots is: