Question

A padlock has a four-digit code that includes digits from 0 to 9, inclusive.

What is the probability that the code does not consist of all odd digits if the same digit is not used more than once in the code?

120 out of 5,040
120 out of 3,024
2,904 out of 3,024
4,920 out of 5,040

Answer 1

Total codes (no repetition) = P(10,4) = 10·9·8·7 = 5,040.

All-odd codes: choose and arrange 4 of the 5 odd digits = P(5,4) = 5·4·3·2 = 120.

So codes that are not all odd = 5,040 − 120 = 4,920. Answer: 4,920 out of 5,040.