Question 1085713
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How many numbers of four different digits each can be 
formed from the digits 0,2,3,5,6,9? 

There are 5 ways to choose the 1st digit. (can't choose 0)
There are 5 remaining ways to choose the 2nd digit. (can choose 0)
There are 4 remaining ways to choose the 3rd digit.
There are 3 remaining ways to choose the 4th digit.

answer: 5&#8729;5&#8729;4&#8729;3 = 300 ways. 
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Of these numbers, how many are even? 
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Case 1.  0 is chosen for the 4th digit.

There is 1 way to choose the 4th digit. (as 0)
There are 5 remaining ways to choose the 1st digit.
There are 4 remaining ways to choose the 2nd digit.
There are 3 remaining ways to choose the 3rd digit.

answer for case 1: 1&#8729;5&#8729;4&#8729;3 = 60 ways. 

Case 2.  0 is not chosen for the 4th digit.

There are 2 ways to choose the 4th digit. (as 2 or 6)
There are 4 remaining ways to choose the 1st digit.  (can't choose 0)
There are 4 remaining ways to choose the 2nd digit.
There are 3 remaining ways to choose the 3rd digit.

answer for case 2: 2&#8729;4&#8729;4&#8729;3 = 96 ways.

Total for the two cases: 60+96 = 156
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how many are divisible by 5?
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Case 1.  0 is chosen for the 4th digit.

Same as case 2 in the preceding problem:

answer for case 1: 60 ways. 

Case 2.  5 is chosen for the 4th digit.

There is 1 way to choose the 4th digit. (as 5)
There are 4 remaining ways to choose the 1st digit. (can't choose 0)
There are 4 remaining ways to choose the 2nd digit.
There are 3 remaining ways to choose the 3rd digit.

answer: 1&#8729;4&#8729;4&#8729;3 = 48 ways.

Total for the two cases: 60+48 = 108 ways.

Edwin</pre></b></font>