organized counting: rolling dice, picking cards, T/F tests,

xo_caroline_xo said:

i have 4 question in my data management course which i dont clearly understand and i was wondering if anyone could help me, or even give me some advice in finishing my assignment...here are the questions;

2. In how many ways can you roll either a sum of 4 or a sum of 11 with a pair of dice?

There are \(\displaystyle 6^{2}\) possible outcomes with 2 dice. You can list them out and count or you could show off and use the generating functions

\(\displaystyle \L\\\left(\sum_{p=1}^{6}{x^{p}}\right)^{2}\)

Now, in the expanded expression, find the coefficients which go with the exponents 4 and 11.

We find \(\displaystyle x^{12}+2x^{11}+3x^{10}+4x^{9}+5x^{8}+6x^{7}+5x^{6}+4x^{5}+3x^{4}+2x^{3}+x^{2}\)

Pretty cool, huh?.

3. In how many ways can you draw a 6 or a face card from a deck of 52 playing cards?

There are 4 different 6's and 12 face cards. Any thoughts?.

8. A standard die is rolled five times. How many different outcomes are possible?

Well, if \(\displaystyle 6^{2}\) outcomes are possible with 2 dice, how many are possible with 5?.

10. In how many ways can a student answer a true-false test that has six questions. Explain your reasoning.

Same principle as the dice problem.

anyone who can help me would be appreciated, thanks!!

caroline

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galactus said:

3. In how many ways can you draw a 6 or a face card from a deck of 52 playing cards?
There are 4 different 6's and 4 face cards. Any thoughts?.

Click to expand...