Question

A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated.

What is the approximate probability that the code only contains odd numbers?

0.0005
0.00099
0.012
0.02381

Answer 1

There are P(10,4) = 10·9·8·7 = 5040 possible distinct 4-digit codes.
Favourable codes use 4 distinct odd digits from {1,3,5,7,9}: P(5,4) = 5·4·3·2 = 120.
Probability = 120/5040 = 1/42 ≈ 0.02381.

Answer: 0.02381.