Question

The number of ways to arrange six examination papers so that best and worst papers appear together are….

Answer 1

Hint: We are given that there are 6 papers in total. These papers consist of best and worst papers too. So from 6 papers 2 papers are of this category. Now we have to find the ways in which these best and worst papers will appear together. So we will make a group of the best and worst papers. So there are 5 papers now. Thus we will use a factorial formula to find the number of ways.

Complete step-by-step answer:
Given are six examination papers. So in general we can say there are 6! Ways to arrange them.
But there is a condition given like best and worst papers appear together.
So now we can say that, there are \[5! \times 2!\] ways in which the papers can be arranged so that best and worst appear together.
\[5! \times 2! = 120 \times 2 = 240\]
Thus we can arrange the papers in 240 different ways.
So, the correct answer is “240 different ways”.

Note: Note that, if they ask this question but in a way the best and worst will never come together then we will subtract the above ways from the total number of ways the paper can be arranged.
Like \[6! - \left( {5! \times 2!} \right)\]
Where 6! Is the total number of ways in which the papers can be arranged.
It is the best approach to find the always together and never appear together condition. If asked for always together we can find the way above. And if asked never together then remove the always appear from all the possible ways.