Disha Expert Team Solutions for Chapter: Permutation & Combination and Probability, Exercise 1: Exercise

If the letters of the word $\mathrm{DIRECTOR}$ are arranged in such a way that all the vowels come together. Find out the total number of ways for making such an arrangement.

Three squares of a chessboard are chosen at random, the probability that two of them are of one colour and one of another is _____.

An old person forgets the last two digits of a telephone number, remembering only that these are different and dialled at random. The probability that the number is dialled correctly is

Each of A and B tosses two coins. What is the probability that they get an equal number of heads? 

A speaks truth in $75\%$ of the cases and B in $80\%$ of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact?

From eighty cards numbered $1$ to $80$, two cards are selected randomly. The probability that both the cards have the numbers divisible by $4$ is given by:

If $A$ and $B$ are two events such that $P\left(A\right)= 0.5, P\left(B\right) = 0.6$ and $P(A \cup B) = 0.8$. Find $P\left(\frac{A}{B}\right)$?

A bag contains$3$ black, $4$ white and $2$ red balls, all the balls being different. The probabilty of picking $6$ balls containing balls of all the colours is: