Are These Solutions to Counting Problems Correct?

[Magotine]

Hi,

I've done more questions. Hopefully the wordings on these word problems aren't vague.

Could someone take a look? I'm not sure if I've thought about the problem the right way.

Thanks v. much in advance.

 

[arildno]

Try to learn LATEX, don't use the doc-format

 

[0rthodontist]

In the first one, the confusion is that you only need 5 letters to define a 9 letter palindrome. If you know the first 5 letters are ABCDE, then you know the last 4 letters are DCBA. So you only get to choose the first 5 letters, so that's how many possibilities there are.

In the second one, count the number of bridges available at each step. First step: 3 bridges. Second step: 4 bridges. Third step (going back): three bridges because you can't use the one you came on. Fourth step: 2 bridges