On her vacations Veena visits four cities $(A,\,B ,\, C$ and $D$ ) in a random order. What is the probability that she visits $A$ first and $B$ last ?
On her vacations Veena visits four cities $(A,\,B ,\, C$ and $D$ ) in a random order. What is the probability that she visits $A$ first and $B$ last ?
$S=\left\{\begin{array}{l}A B C D, A B D C, A C B D, A C D B, A D B C, A D C B, \\ B A C D, B A D C, B D A C, B D C A, B C A D, B C D A \\ C A B D, C A D B, C B D A, C B A D, C D A B, C D B A, \\ D A B C, D A C B, D B C A, D B A C, D C A B, D C B A\end{array}\right.$
Let $G$ be the event "she visits $A$ first and $B$ last" $^{\prime \prime}$
$G=\{A C D B, A D C B\}$
So, $n(G)=2$
$P(G)=\frac{n(G)}{n(S)}$ $=\frac{2}{24}=\frac{1}{12}$
Similar Questions
A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is $1/4$ and that of the woman's selection is $1/3$. What is the probability that none of them will be selected
A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is $1/4$ and that of the woman's selection is $1/3$. What is the probability that none of them will be selected
Consider the set of all $7-$digit numbers formed by the digits $0,1,2,3,4,5,6$, each chosen exactly once. If a number is randomly drawn from this set, the probability that it is divisible by $4$ is
Consider the set of all $7-$digit numbers formed by the digits $0,1,2,3,4,5,6$, each chosen exactly once. If a number is randomly drawn from this set, the probability that it is divisible by $4$ is
- [KVPY 2021]
Choose a number $n$ uniformly at random from the set $\{1,2, \ldots, 100\}$. Choose one of the first seven days of the year $2014$ at random and consider $n$ consecutive days starting from the chosen day. What is the probability that among the chosen $n$ days, the number of Sundays is different from the number of Mondays?
Choose a number $n$ uniformly at random from the set $\{1,2, \ldots, 100\}$. Choose one of the first seven days of the year $2014$ at random and consider $n$ consecutive days starting from the chosen day. What is the probability that among the chosen $n$ days, the number of Sundays is different from the number of Mondays?
- [KVPY 2014]
From a well shuffled pack of cards one card is drawn at random. The probability that the card drawn is an ace is
From a well shuffled pack of cards one card is drawn at random. The probability that the card drawn is an ace is
On her vacations Veena visits four cities $(A,\,B ,\, C$ and $D$ ) in a random order. What is the probability that she visits $A$ before $B$ and $B$ before $C ?$
On her vacations Veena visits four cities $(A,\,B ,\, C$ and $D$ ) in a random order. What is the probability that she visits $A$ before $B$ and $B$ before $C ?$