Question

In a school there are four sections of 40 students each in XI standard. In how many ways can a set of 4 student representatives be chosen one from each section?

Answer 1

Hint:As it is given that there are 4 sections and in each section there are 40 students, so we have to choose 1 student from the each section using the formula ${}^{n}{{C}_{r}}=\dfrac{n!}{\left( n-r \right)!r!}$, and if we find for one section then we just have to multiply it 4 times to get the final answer.

Complete step-by-step answer:
Let’s start our solution,
Combination means that in how many ways we can choose from the given number of objects.Now if we have n different objects and from them we need to pick r objects, then the formula is
${}^{n}{{C}_{r}}=\dfrac{n!}{\left( n-r \right)!r!}$
Now for one section we have n = 40 and r = 1,
Hence, substituting the values in ${}^{n}{{C}_{r}}=\dfrac{n!}{\left( n-r \right)!r!}$ we get,
$\begin{align}
  & =\dfrac{40!}{1!\left( 40-1 \right)!} \\
 & =\dfrac{40\times 39!}{39!} \\
 & =40 \\
\end{align}$
Now we have found the value of the number of ways of choosing a student representative from one section, so for the other section it will be the same.
Hence, the answer will be ${{\left( 40 \right)}^{4}}=2560000$.

Note:Here keep in mind that we are not using the formula of permutation because we just have to select the students, the order in which they are selected doesn’t matter, hence this point must be kept in mind so that there will not be any mistake.