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# Disrete Maths watch

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.

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