A hint to get started
Allow leading zero in a six-position PIN
Joshua tries to recall the 6-digit PIN number for his ATM card. Assume 000000 is even and valid. How many possible numbers can there be if he remembers that:
(i) the number starts and ends with the digit 5? mark
(ii) the number is odd and the digits do not repeat? marks
(iii) the digits do not repeat and there are exactly 3 odd digits? marks
[2011/PJC/II/10]
CJC · Review problems · Question 3
A PIN is a fixed-length string; its first digit may be zero.