Perms and combs (1 Viewer)

[Average Boreduser]

guys
help
pls

 

[Average Boreduser]

ans = c

 

[carrotsss]

you start by laying out the letters of the word press. then, we fill in the rest of the letters between the letters of press, so:
XPXRXEXSXSX where X are places we can put a letter.

For O, we’ve got 6 options for where to put it. If, wlog, we put it in the first spot, we end up with this for our next letter: XIXPXRXEXSXSX. So we’ve created another space for a letter. So then there are 7 options for the next letter, and likewise 8 for the next, and then 9 for the next, and 10 for the next after that, all divided by 2 factorial since there are 2 Is

this gives B, so I don’t really know why the answer would be C

 

[Average Boreduser]

you start by laying out the letters of the word press. then, we fill in the rest of the letters between the letters of press, so:
XPXRXEXSXSX where X are places we can put a letter.

For O, we’ve got 6 options for where to put it. If, wlog, we put it in the first spot, we end up with this for our next letter: XIXPXRXEXSXSX. So we’ve created another space for a letter. So then there are 7 options for the next letter, and likewise 8 for the next, and then 9 for the next, and 10 for the next after that, all divided by 2 factorial since there are 2 Is

this gives B, so I don’t really know why the answer would be C

exactly, idfk what they were trying to say here :

 

[Average Boreduser]

oh wait shit nvm the answer is b

 

[Drongoski]

It is indeed B.

 

[funnytomato]

Alternatively think about how many arrangements without any restriction and then out of all what proportion has PRESS exactly in this order:

10!/(2!*2!) * 2!/5!

 

[Luukas.2]

Another approach:

• Arrange the IMION in 5! / 2! ways.
• Choose the 5 positions from 10 for the word PRESS in 10C5 = 10! / (5!)² ways
• Total arrangements = 10! / (5!)² times 5! / 2! = 10!5! / (5!)²2! = 10! / 5!2! after cancelling

Thus, the answer is indeed (B)