Counting & Binomial Thrm

Question 1

What formula should you use if you’re asked about counting the ways a groups (split into two subgroups) can be counted?

Answer 1

• m: total members of subgroup of interest
• n: total members of the other subgroup
• k: total number of members you will choose
• x: number of members you want to choose from the subgroup of interest

Question 2

What are the steps to finding the correct “r” that gives the term of interest in a binomial expansion?

Answer 2

1. Plug in all of the values you know into the “general term” of the binomial expansion.
2. Extract only the “x”s (no coefficients)
3. Set this expression equal to the x term you’re supposed to find.
4. Solve for r.
5. Go back and plug this r into the expression from step 1.

Question 3

How can you add together different “choose” terms?

For example,

Answer 3

You rewrite them in the fractional factorial forms and then separate the factorials until you can find the common denominator.

Once you combine the fraction, see how to rewrite it as a combination.