Library / UKMT Senior Kangaroo /115 of 139

UKMT Senior Kangaroo, 2020

Combinatorics Difficulty 3.0 AMC 10/12 Prove it United Kingdom

A random number generator gives outputs of $1, 2, 3, 4$ and $5$ with equal probability. The values of $a$ , $b$ and $c$ are each chosen by running the generator once. The probability that $a \times b + c$ is even can be written as a fraction in its lowest terms as $\frac{N}{D}$ . What is the value of $10N + D$ ?

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.