antoniogmat wrote:
I can't understand the result. This is my approach:
If Dave finishes 6th, Austin can finish in 5 positions (1st to 5th)= 5
If Dave finishes 5th, Austin can finish in 4 positions (1st to 4th)= 4
.
.
.
If Dave finishes 1st, Austin cannot finish in a better position.
Therefore, 5*4*3*2*1=5!=120
Could please someone explain where I am mistaken and why answer b is not correct?
Thank you!
You have gone wrong in your approach.
1) If D is 6th and A is 5th, remaining 4 can be in 4! ways. As A can be in 4, 3, 2 or 1st position, we can take it as with D in 6th position, A can be in any of 5 positions and remaining 4 in 4! ways. => 5*4!
2) Similarly when D is in 5th position, A can take any of the top 4 positions and remaining 4 will take 4! ways. => 4*4!
3) When D is in 4th position => 3*4!
Total : 5!+4*4!+3*4!+2*4!+1*4!=4!(5+4+3+2+1)=24*15=360
Hope it clears your query.
Thank you very much for your help, I have it much clearer now.