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    Can somebody please help me with this question:
    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|
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    (Original post by Harriettttttt1)
    Can somebody please help me with this question:
    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 A_i should be?
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    Well I thought it should be one of the letters appearing at least once but I don't really know
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    (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 A_i as "letter i does not appear".
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    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?
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    (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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