Five persons enter a lift cabin in the cellar of a $7$-floor building (excluding the cellar). If each of them independently and with equal probability can leave the cabin at any floor out of the $7$ floors (beginning with the first), then the probability that all $5$ persons leave the cabin at different floors is:
- A$\frac{360}{2401}$
- B$\frac{5}{54}$
- C$\frac{51}{71}$
- D$\frac{5}{18}$
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$A$ four-digit number is to be formed using the digits $1, 2, 3, 4, 5, 6, 7$ (no digit is repeated). What is the probability that the number formed is $> 4000$?
$A$ bag contains $6$ red,$5$ white and $4$ black balls. Two balls are drawn. The probability that none of them is red,is
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View Solution$A$ bag contains $4$ red, $3$ white, and $5$ blue balls. Three balls are drawn at a time randomly from the bag. Match the items from List-$I$ with those of List-$II$.
List-$I$ List-$II$ $A$. Probability of getting $1$ red, $1$ white and $1$ blue ball $(i)$ $\frac{3}{44}$ $B$. Probability of getting $2$ white and $1$ blue ball $(ii)$ $\frac{21}{55}$ $C$. Probability of getting $2$ red and $1$ white ball $(iii)$ $\frac{38}{55}$ $D$. Probability that none of the balls is white $(iv)$ $\frac{3}{11}$ $(v)$ $\frac{9}{110}$
| List-$I$ | List-$II$ |
| $A$. Probability of getting $1$ red, $1$ white and $1$ blue ball | $(i)$ $\frac{3}{44}$ |
| $B$. Probability of getting $2$ white and $1$ blue ball | $(ii)$ $\frac{21}{55}$ |
| $C$. Probability of getting $2$ red and $1$ white ball | $(iii)$ $\frac{38}{55}$ |
| $D$. Probability that none of the balls is white | $(iv)$ $\frac{3}{11}$ |
| $(v)$ $\frac{9}{110}$ |
$A$ bag contains $6$ red, $2$ white and $8$ blue balls. Three balls are drawn at random from the bag. Match the items of List-$I$ with those of List-$II$.
$A$. Probability that none of the balls is white $I$. $\frac{1}{70}$ $B$. Probability of getting $2$ white and $1$ blue ball $II$. $\frac{6}{35}$ $C$. Probability of getting $2$ blue and $1$ white ball $III$. $\frac{13}{20}$ $D$. Probability of getting $1$ red, $1$ white and $1$ blue ball $IV$. $\frac{1}{10}$
| $A$. Probability that none of the balls is white | $I$. $\frac{1}{70}$ |
| $B$. Probability of getting $2$ white and $1$ blue ball | $II$. $\frac{6}{35}$ |
| $C$. Probability of getting $2$ blue and $1$ white ball | $III$. $\frac{13}{20}$ |
| $D$. Probability of getting $1$ red, $1$ white and $1$ blue ball | $IV$. $\frac{1}{10}$ |
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