Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

1) A businessman has 10 suits. He needs to pack 3 of them to go on a trip. How many can he do this?

2) A multiple choice test has 8 questions, each with 3 possible answers. how many can the test be filled?

3) I order a dozen bagels. there are poppy seed, onion and sesame bagels available today. in how many different ways can I fill my order?

4) A bag contains 26 scrabble tiles, each with a different letter on it. i draw 3 tiles and arrange them on the tray in front of me. How many "words" can I form this way?

1) 10 choose 3
2) 8 choose 3
4) $5!$

Is my thinking correct?

share|cite|improve this question
When answering questions such as these, it's best to provide an explanation as to why there's e.g. $\binom{10}{3}$ ways (rather than some other formula involving $10$ and $3$). – Douglas S. Stones Apr 15 '13 at 17:03
  1. Your answer is correct.
  2. Each answer can independently be chosen in 3 ways. So the total number of ways is $3^8$.
  3. Your answer is incorrect. (See the comment below.)
  4. Three tiles could be drawn in $\binom{26}{3}$ ways, and there are $3!$ ways to permute them after drawing. So total no. of ways is $3!\binom{26}{3}$.
share|cite|improve this answer
I don't agree with 3. You just need to count the number of solutions of $p + o + s = 12$, where $p,o,s \ge 0$ and integers. Otherwise poppy 11x + sesame is counted differently as sesame plus poppy 11x, e.g. – Henno Brandsma Apr 15 '13 at 14:24
Yes. That is a mistake. I am removing it. – Shahab Apr 15 '13 at 14:25
So would it be 12!/4!4!4!? – hjg hjg Apr 15 '13 at 14:32… – Shahab Apr 15 '13 at 14:34
(3) is equivalent saying how many ways can you put 12 indistinguish balls into 3 distinguish boxes. By using the the distribution rule $\binom{n+k-1}{n}$ where $n$ is the number of balls, and $k$ is the number of boxes, so, the solution is simply $\binom{12+3-1}{12}$ – user62453 Apr 15 '13 at 16:04

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.