Answer: 160
Solution:
First digit can be: 5, 6, 7 (3 variants totally).
Second digit can be: any (7 variants totally).
Third digit can be: any (7 variants totally).
Fourth digit can be: 2,4,6 (3 variants totally).
If the first digit is 5, than there are 3 ways to choose the fourth digit, 5 ways to choose the third digit, 4 ways to choose the second digit.
If the first digit is 6, than there are 2 ways to choose the fourth digit, 5 ways to choose the third digit, 4 ways to choose the second digit.
If the first digit is 7, than there are 3 ways to choose the fourth digit, 5 ways to choose the third digit, 4 ways to choose the second digit.
Overall:
"Number=3\u00d75\u00d74\\,+\\,2\u00d75\u00d74\\,+\\,3\u00d75\u00d74=60+40+60=160"
Comments
Other cases can be explained in a similar way.
The number is bigger than 5000. Let the first digit be 5, a fixed digit. Because the code must be even, then 3 choices are possible for the fourth digit because only 2, 4, 6 are even digits among digits 1 to 7. Because the digits cannot be repeated and two digits for the first and the fourth places have already been selected, then 7-2=5 choices are possible for the second digit. Finally, the third digit can be chosen in 5-1=4 ways because the digits cannot be repeated.
Hi,thanks for the answer.Im not sure about the choices for the second,third and fourth digits?please explain to me
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