<s>[INST] How many even numbers of four digits can be formed with the digits 0,1,2,3,4,5 and 6 no digit being used more? My attempt to solve this problem is:
First digit cannot be zero, so the number of choices only $6 (1,2,3,4,5,6)$
The last digit can be pick from $0,2,4,6$, so the number of choices only 4
Second digit can be only pick from the rest, so the number of choices only 5
Third digit can be only pick from the rest, so the number of choices only 4
The total number of choices is $6\cdot 4\cdot 5\cdot 4= 480$
So, is my solution true? Or I miss something?
Thanks
 [/INST] For an even no. last digit needs to be even = 4 choices
Total 4 digit even numbers = (Total even numbers) - (Total 3 digit even numbers)
Total even numbers: $4\cdot 6\cdot 5\cdot 4 = 480$
Total 3-digit even numbers: $3\cdot 5\cdot 4\cdot 1 = 60$
Total 4-digit even numbers: $480 - 60 = 420$
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