Question

22 Liam is trying to remember a 3-digit code.

He knows the rule that

the first digit is a cube number

the second digit is a factor of 16

the third digit is an odd number.

Liam tries at random a code that matches the rule.

Work out the probability that this is the correct code.

Answer 1

The first digit may be $1$ or $8.$ The second digit may be $1,2,4,8.$ The third digit may be $1,3,5,7,9.$

There are $2\times4\times5=40$ variants.

The probability that this is the correct code is $\dfrac{1}{40}.$