Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

In how many ways $25$ students of a class can be divided into $5$ teams such that a section contains $5$ students in each team.
Option: 1
$5194672859300$

Option: 2
$5194672859370$

Option: 3
$5194672859376$

Option: 4
$5194672859300$

Answers (1)

best_answer

The given information is:

Number of students in a class $=25$

Number of teams $=5$

Number of students in each teams $=5$

Pick first $5$ students from $25$ students,

Total no. of ways of choosing is:

$\frac{25 !}{(25-5) ! 5 !}=\frac{25 !}{20 ! 5 !}=53130$

Pick next $5$ students from $20$ students,

Total no. of ways of choosing is:

$\frac{20 !}{(20-5) ! 5 !}=\frac{20 !}{15 ! 5 !}=15504$

Pick next $5$ students from $15$ students,

Total no. of ways of choosing is:

$\frac{15 !}{(15-5) ! 5 !}=\frac{15 !}{10 ! 5 !}=3003$

Pick next $5$ students from $10$ students,

Total no. of ways of choosing is:

$\frac{10 !}{(10-5) ! 5 !}=\frac{10 !}{5 ! 5 !}=252$

Pick last $5$ students from remaining $5$ students and the number of ways this can be done is $1$ .

Since the five groups are similar, there is no differentiation between them. Therefore, we need to divide it with $5 !=120$ .

The total numbers of ways:

$\frac{53130 \times 15504 \times 3003 \times 252}{120}=5194672859376$

Posted by

Gautam harsolia

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question