You are Here: Home >< Maths

Disrete Maths

Announcements Posted on
Last day to win £100 of Amazon vouchers - don't miss out! Take our quick survey to enter 24-10-2016
consider the set of all possible 5-letter strings using the letters ZAP. By
considering an appropriate choice of Ai and using (1), count the number
of such strings that use each of the three letters at least once.

I know I should use inclusion/exclusion principle but all I have been able to find is that the number with at least one Z(orAorP) is 211. so |Ai| 211, I have no idea how to find |A1UA2UA3| or |Ai n Aj|
2. (Original post by Harriettttttt1)
consider the set of all possible 5-letter strings using the letters ZAP. By
considering an appropriate choice of Ai and using (1), count the number
of such strings that use each of the three letters at least once.

I know I should use inclusion/exclusion principle but all I have been able to find is that the number with at least one Z(orAorP) is 211. so |Ai| 211, I have no idea how to find |A1UA2UA3| or |Ai n Aj|
What do you think the event should be?
3. Well I thought it should be one of the letters appearing at least once but I don't really know
4. (Original post by Harriettttttt1)
Well I thought it should be one of the letters appearing at least once but I don't really know
Think about having event as "letter i does not appear".
5. Ok, so now I've got |Ai|=32
|Ai n Aj|=1 |Ai n Aj n Ak|=0
so |Ai U Aj U Ak|=93
Ans= 3*5 -93=150
Is this right?
6. (Original post by Harriettttttt1)
Ok, so now I've got |Ai|=32
|Ai n Aj|=1 |Ai n Aj n Ak|=0
so |Ai U Aj U Ak|=93
Ans= 3*5 -93=150
Is this right?
Looks OK to me.

Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: April 22, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

How does exam reform affect you?

From GCSE to A level, it's all changing

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read here first

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants