If a group of six students including two part | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Total number of ways to arrange $6$ students in a row $= 6! = 720$.To find the number of favorable arrangements, consider $A$ and $B$ with one stu

Vedclass · Accepted Answer

$\frac{4}{15}$

Vedclass · Answer

(B) Total number of ways to arrange $6$ students in a row $= 6! = 720$.To find the number of favorable arrangements, consider $A$ and $B$ with one student between them as a single block. There are $4$ remaining students. We choose $1$ student out of $4$ to place between $A$ and $B$ in $^4C_1$ ways.Now, treat the block $(A, 	ext{student}, B)$ as one unit. Along with the remaining $3$ students, we have $4$ units to arrange, which can be done in $4!$ ways.Within the block, $A$ and $B$ can be arranged in $2!$ ways (i.e.,$A, 	ext{student}, B$ or $B, 	ext{student}, A$).Number of favorable arrangements $= ^4C_1 	imes 4! 	imes 2! = 4 	imes 24 	imes 2 = 192$.Probability $= \frac{192}{720} = \frac{4}{15}$.

If a group of six students including two particular students $A$ and $B$ stand in a row, then the probability of getting an arrangement in which $A$ and $B$ are separated by exactly one student in between them is

Similar Questions

In how many ways can $5$ boys and $3$ girls sit in a row so that no two girls are together?

$A$ parallelogram is cut by two sets of $m$ lines parallel to its sides. The number of parallelograms thus formed is

Let $T_n$ denote the number of triangles which can be formed using the vertices of a regular polygon of $n$ sides. If $T_{n+1} - T_n = 21$,then $n$ equals

The number of triangles that can be formed by choosing the vertices from a set of $12$ points,$7$ of which lie on the same straight line,is

If the number of rectangles formed on a chessboard is $1296$,then the total number of squares formed on the chessboard is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module