Q:

How many ways can a from be filled out?

In a survey, viewers are given a list of 20 TV programmes. They are asked to label their three
favourites 1, 2 and 3, and to put a tick against those they have heard of (if any) from the
remaining 17. In how many ways can the form be ﬁlled out? (Assume that everyone has three
favourite programmes to nominate.)

A:

Choose favourite 1... $20$ ways
Choose favourite 2... $19$ ways
Choose favourite 3... $18$ ways
For each of the 17 remaining programmes decide whether or not to tick it... $2^{17}$ ways
So answer is $20*19*18*2^{17}$

