Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.)

share|cite|improve this question
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 $20*19*18*2^{17}$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.