10 examination papers are arranged in such a way that the best and worst papers never come tog.The number of arrangement is..??
Answers
If 10 examination papers are arranged in such a way that the best and worst papers never come tog, then the number of arrangement is 8 * 9! or 2903040.
Step-by-step explanation:
There are a total of 10 examination papers.
So, the total no. of arrangements in which, all the 10 examination papers are arranged without any condition = 10! Ways.
Case 1:
Now, let’s see the no. of arrangements that can be done if the best and the worst papers come together.
For this case, we can consider the best and the worst papers to be one, so, the no. of arrangements will be = 10! – 1! = 9! Ways
Also, the best and the worst can be arranged in 2 different ways themselves i.e., [best & worst] or [worst & best].
∴ No. of ways 10 examination papers can be arranged, when the best and the worst papers come together = 2! * 9! Ways
Case 2:
Thus,
The no. of ways 10 examination papers can be arranged when the best and worst papers never come together is,
= 10! – [2! * 9!]
= [10*9!] – [2*1*9!]
= 9! [10 - 2]
= 9! * 8
= 9*8*7*6*5*4*3*2*8
= 2903040
Hope this is helpful!!!!!!
Answer:
8*9!
Step-by-step explanation:
there are 10 examination papers = 10!ways
when the best and worst papers come together, regarding 2 papers as 1 paper, we have only 9 papers.
Those papers can be arranged in 2! ways
when both are not together
=10! - 9!* 2!
9! (10-2)
8*9!