Q21 / 60 · JEE Advanced 2014 (Paper 2) · Mathematics

Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is atleast one more than the number of girls ahead of her is

Correct answer
A
$\frac{1}{2}$
B
$\frac{1}{3}$
C
$\frac{2}{3}$
D
$\frac{3}{4}$

Solution

Either a girl start the sequence or will be at second position and will not acquire the last position as well.
Required probability

= \frac{(^{3} C_{2} \times 2! \times 3! +^{2} C_{1} \times 2! \times 3!)}{5!} = \frac{1}{2}

Hence, the correct answer is option: 'A'.

Relevant Questions

A group of 9 students, , is to be divided to from three teams , and of sizes 2,3 , and 4 , respectively. Suppose that cannot be selected for2024 (Paper 1)Arrangement under Constraint
Let X be the set of all five digit numbers formed using 1 , 2 , 2 , 2 , 4 , 4 , 0 . For example, 22240 is in X while 02244 and 44422 are not2023 (Paper 2)Arrangement under Constraint
The number of 4 -digit integers in the closed interval 2022 , 4482 formed by using the digits 0 , 2 , 3 , 4 , 6 , 7 is ______.2022 (Paper 1)Arrangement under Constraint
An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two vis2020 (Paper 2)Arrangement under Constraint
Five persons A , B , C , D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue 2019 (Paper 2)Arrangement under Constraint
The number of 5 digit numbers which are divisible by 4 , with digits from the set { 1,2 , 3,4 , 5 } and the repetition of digits is allowed,2018 (Paper 1)Arrangement under Constraint