Four distinct numbers are randomly selected out of the set of first $20$ natural numbers. Probability that no two of them are consecutive is -
$\frac{28}{57}$
$\frac{20}{63}$
$\frac{19}{93}$
$\frac{12}{59}$
A bag contains $5$ black balls, $4$ white balls and $3$ red balls. If a ball is selected randomwise, the probability that it is a black or red ball is
From a group of $10$ men and $5$ women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is
A bag contains tickets numbered from $1$ to $20$. Two tickets are drawn. The probability that both the numbers are prime, is
All face cards from pack of $52$ playing cards are removed. From remaining $40$ cards two are drawn randomly without replacement, then probability of drawing a pair (same denominations) is
Among $15$ players, $8$ are batsmen and $7$ are bowlers. Find the probability that a team is chosen of $6$ batsmen and $5$ bowlers