The number lock of a suitcase has $4$ wheels, each labelled with ten digits i.e., from $0$ to $9 .$ The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?
The number lock has $4$ wheels, each labelled with ten digits i.e., from $0$ to $9 .$
Number of ways of selecting $4$ different digits out of $10$ digits $=^{10} C_{4}$
Now, each combination of $4$ different digits can be arranged in $\lfloor 4$ ways.
$\therefore$ Number of four digits with no repetitions $=^{10} C_{4} \times\left\lfloor 4=\frac{\lfloor {10}}{\lfloor {4\lfloor 6}} \times\lfloor 4=7 \times 8 \times 9 \times 10=5040\right.$
There is only one number that can be open the suitcase.
Thus, the required probability is $\frac{1}{5040}$.
A bag contains $3$ red, $4$ white and $5$ black balls. Three balls are drawn at random. The probability of being their different colours is
Six points are there on a circle . Two triangles are drawn with no vertex common. What is the probability that none of the sides of the triangles intersect
A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is $q$. If $p : q = m$ $: n$, where $m$ and $n$ are coprime, then $m + n$ is equal to $..........$.
In a relay race there are five teams $A, \,B, \,C, \,D$ and $E$. What is the probability that $A,\, B$ and $C$ are first three to finish (in any order) (Assume that all finishing orders are equally likely)
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