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.)

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Yes.${}{}{}{}{}$ – anon Jun 19 '12 at 8:06
Thanks! I changed this to answer my own question. – MinaHany Jun 19 '12 at 8:13

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 $20*19*18*2^{17}$