Question

Over the past week, an airline pilot was n Vancouver three days, Calgary two days, Whitehorse one day, and Winnipeg two days.

a) How many different itineraries could the pilot have had?

b) If you knew that the two days in Calgary were consecutive (a layover), how many itineraries could the pilot have had?

I figured out A..
8! / 3!2!1!2! = 1680 different itineraries..
but i don't understand what the consecutive part for B means.

Answer 1

In effect what you were doing in a) was to find the number of arrangements of
V,V,V,C,C,WH,WI,WI

What it says in b) is that the C,C have to be side by side in the arrangement.
One way to do this is to consider C,C as a single element, so now you have 7 things to arrange instead of 8, you still have 3 V's, 2 WI's

so for b)
no of ways = 7!/(3!2!) = 420