A fair dice is thrown up to $20$ times. The probability that on the $10^{th}$ throw, the fourth six apears is :-
$\frac{{84 \times {5^6}}}{{{6^{10}}}}$
$\frac{{112 \times {5^6}}}{{{6^{10}}}}$
$\frac{{84 \times {5^6}}}{{{6^{20}}}}$
None
The probability that the three cards drawn from a pack of $52$ cards are all red is
There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, is a random order till both the faulty machines are identified. Then the probability that only two tests are needed is
From a group of $7$ men and $4$ ladies a committee of $6$ persons is formed, then the probability that the committee contains $2$ ladies is
Two cards are drawn at random from a pack of $52$ cards. The probability that both are the cards of spade is
A pack of cards contains $4$ aces, $4$ kings, $4$ queens and $4$ jacks. Two cards are drawn at random. The probability that at least one of these is an ace, is