If $7$ dice are thrown simultaneously, then probability that all six digit appears on the upper face is equal to -
$\frac{{35}}{{{6^3} \times 3}}$
$\frac{6}{{{}^{12}{C_5}}}$
$\frac{{70}}{{{6^3} \times 3}}$
$\frac{6}{{{}^{12}{C_6}}}$
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 committee, is
Two numbers are selected randomly from the set $S = \{ 1,\,2,\,3,\,4,\,5,\,6\} $ without replacement one by one. The probability that minimum of the two numbers is less than $4$ is
There are $10$ engineering colleges and five students $A, B, C, D, E$ . Each of these students got offer from all of these $10$ engineering colleges. They randomly choose college independently of each other. Tne 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
Let $X$ be a set containing $n$ elements. If two subsets $A$ and $B$ of $X$ are picked at random, the probability that $A$ and $B$ have the same number of elements, is
A bag contains $6$ white and $4$ black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is: