The fundamental counting principle

[kris.yarmak123]

Hello. We have just started a new unit on permutations and counting principle, and I am stuck ok these two questions? Can someone please explain me how do I solve #4,5?

 

[pka]

Hello. We have just started a new unit on permutations and counting principle, and I am stuck ok these two questions? Can someone please explain me how do I solve #4,5?

For #4 consider the three empty boxes \(\displaystyle \boxed{\;\;\;}~\boxed{\;\;\;}~\boxed{\;\;\;}\)
Use the simple multiplication principle. You have six choices the first box. five for the second, etc.

For #5 you have six choices for each box.

According to our rules, you must post what you do.

 

[Dr.Peterson]

Hello. We have just started a new unit on permutations and counting principle, and I am stuck ok these two questions? Can someone please explain me how do I solve #4,5?

Can you tell us in what way you are stuck? Show us something that you tried (or tried to try!), and tell us what makes these problems different from the ones you can do.

 

[kris.yarmak123]

For #4 consider the three empty boxes \(\displaystyle \boxed{\;\;\;}~\boxed{\;\;\;}~\boxed{\;\;\;}\)
Use the simple multiplication principle. You have six choices the first box. five for the second, etc.

For #5 you have six choices for each box.

According to our rules, you must post what you do.

Thanks, I solved those ones .)

 

[pka]

Thanks, I solved those ones .)

Do you want us to continue to help?
Then post your work. It may help others.

 

[kris.yarmak123]

Do you want us to continue to help?
Then post your work. It may help others.

Yes, here it is
PS. For questions 7 and 9 I am still thinking

 

[kris.yarmak123]

Can you tell us in what way you are stuck? Show us something that you tried (or tried to try!), and tell us what makes these problems different from the ones you can do.

I just have no idea how to do these ones at all, I haven't had the one with cards at all. For 7 , I tried to write 3×2×1=6 since it asks me "how many different arrangements are there of three different letters". And for 9, I know literally nothing so I cannot even provide an attempt

 

[Dr.Peterson]

You got #4 and #5 right. Great!

We'll leave #7 and #9 in the other thread.