Part A

Use a fresh answer book for this part. Show all working-out with your answers. Approved graphing calculators may be used.

It is 4am on a Friday morning and Eirin has been woken by an SMS from the emergency support line. A colocation customer’s server is offline, and she needs to visit the datacentre. Due to sleep-deprivation and/or ethanol intoxication, Eirin is unable to find the lightswitch, but needs to throw on some clothes and get there ASAP.

Her wardrobe contains three skirts {black,black,red}, four tops {purple,blue,black,black} and two pairs of comfortable shoes {black heels,black sneakers}. Each piece of clothing is chosen at random.

1. How many distinct outfits does Eirin have available?
2. What is the probability that Eirin will have a coordinated outfit?
3. How much easier is it to just pick up whatever’s lying on the floor from last night?
4. Will it be faster for her to put her hair in a single french braid, or twintails?
5. What is the probability that the colocation customer has done something totally silly, like changing their firewall configuration and subsequently looking themselves out in the process?
6. How much will Anchor charge the customer for this out-of-hours callout?