If two sections of strengths $30$ and $45$ are formed from $75$ students who are admitted in a school,then the probability that two particular students are always together in the same section 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 . . . . . .

Four cards are drawn at random from a pack of playing cards. The probability of getting exactly two cards from the same suit and the remaining two cards from two different suits 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:

$A$ bag contains $4$ red and $4$ blue balls. Four balls are drawn one by one from the bag. Find the probability that the drawn balls are of alternating colors.

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: