Expert: Ahmed Salami - 6/1/2004

Question
hi, you know how you said for cute integers to go 4*4*4*4? well wouldnt it be 4*5*5*5. because "zero" can also be one of the numbers?
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Followup To
Question -
call an integer "wild" if no two of its digits are equal and no digit is 0. Call an integer “cute” if all its digits are even. how many four-digit integers are either cute or wild?
Answer -
Hi,
I am really sorry for the delay.
Alright then,
Let n(W)= The amount of wild integers
n(W)= 9P4 (read '9 permutation 4')
This is the number of ways of arranging the remaining nine digits (1,2,3,....,9)when 0 has been excluded without repetition of any digit.
n(W)= (9)(8)(7)(6)= 3024
This is evident considering that the first place can be filled in 9 ways,the second in 8 ways, the third in 7 ways and the last in 6 ways.
Let n(C)= The amount of cute integers
n(C)= 4^4
This is the number of ways of arranging the four even digits (2,4,6,8) with repetition allowed.
n(W)= (4)(4)(4)(4)= 256
Let n(WnC)= The amount of integers that are both wild and cute
n(WnC)= 4P4 (read '4 permutation 4')
This is the number of ways of arranging the four even digits (2,4,6,8) without repetition.
n(W)= (4)(3)(2)(1)= 24
Now,using set notation,
n(WUC)= n(W)+ n(C)- n(WnC)
     = 3024 + 256 - 24
     = 3256
This is the nmber of four digit integers that are either cute or wild.  

Answer
Hello Sara,
Well, i didn't consider 0 as an even number. If you consider it as an even number then the amount 4*5*5*5 would in fact be correct and you can then go on to complete the calculations. I was more concerned with the method of achieving the answers.
Anyway, it was very good of you to give me a feedback on the answer.
Would love to hear from you regularly.
Regards.