$A$ 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 three dice are thrown,then the probability that the sum of the numbers on the uppermost faces is at least $5$ is:

If $4$ letters are selected at random from the letters of the word $PROBABILITY$,then the probability of getting a combination of letters in which at least one letter is repeated is

There are $10$ engineering colleges and five students $A, B, C, D, E$. Each of these students received an offer from all of these $10$ engineering colleges. They randomly choose a college independently of each other. The probability that all get admission in different colleges can be expressed as $\frac{a}{b}$,where $a$ and $b$ are co-prime numbers. Then the value of $a + b$ is:

From a group of $50$ students,two sections comprising of $20$ and $30$ students are formed. If $Ram$ and $Rahim$ are two particular students among the $50$ students,then the probability that they both belong to the same section is

If three distinct numbers are selected from the first $100$ natural numbers,what is the probability that all selected numbers are divisible by both $2$ and $3$?