Words with or without meaning are to be formed using all the letters of the word $EXAMINATION.$ The probability that the letter $\mathrm{M}$ appears at the fourth position in any such word is:
$\frac{1}{9}$
$\frac{1}{66}$
$\frac{2}{11}$
$\frac{1}{11}$
Two different families $A$ and $B$ are blessed with equal number of children. There are $3$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket . If the probability that all the tickets go to the children of the family $B$ is $\frac {1}{12}$ , then the number of children in each family is?
A bag contains $4$ white and $3$ red balls. Two draws of one ball each are made without replacement. Then the probability that both the balls are red is
Two integers are selected at random from the set $\{1, 2, …, 11\}.$ Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is
In a relay race there are five teams $A, \,B, \,C, \,D$ and $E$. What is the probability that $A,\, B$ and $C$ are first three to finish (in any order) (Assume that all finishing orders are equally likely)
Two marbles are drawn in succession from a box containing $10$ red, $30$ white, $20$ blue and $15$ orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is