Problems that mention planes, trains, bicycles, distance, mph (rate), and travel terminolgy

Use formula

rate x time = distance

Do not think about how long it takes to do the entire job, but rather how much of the job can be done in one hour. 

Then set that fraction equal to 1/x, so

a/b(fraction of job done in 1 hour) = 1/x

"Function" Problems containing strange symbols

($ or # or * or "delta" or factorials "x!")

Factorials "x!"

5! = ...

= 5 x 4 x 3 x 2 x 1

=120

Put total number of possibilities in the denominator, and the number of possibilities that your are looking for in the numerator.

Probability - One Thing OR Another

Probability of either one thing OR another thing happening

Simply add the probabilites.

Figure out the probability of the first scenario happening.  Then figure out the probability of the second scenario happening.

Ex

1/18 + 3/18 = 4/18 = 2/9

Probability - Odds That

Something Doesn't Happen

Figure out the probability that it WILL happen, and subtract that fraction from 1.

Ex:  Odds of something happening are 4/18.

Odds it wont happen are:

 1 - 4/18 = 14/18 = 7/9

Probability - Odds That

at Least One Thing Will Happen

Use this equation:

The probability of what you WANT to happen plus the probability of what you DON'T want to happen equals one.

So 1 - the probability that all other outcomes will happen = the probability you're looking for.

Combinations

Ex:  3 categories of menu, different possible selections in each category.  How many different combinations (meals) can you oder?

Simple

Multiply the number of choices for each of the categories.

Permutations - Single Source, Order Matters

Choosing from a group of similar items with one slight wrinkle.  Or choosing from same source to fill spots.

Multiply the number of choices for each of the spots, remembering the number of choices keep getting smaller.

Ex:  3 teams, 3 Standings

3 x 2 x 1 = 6

Permutations - Single Source, Order Matters But Only for a Selection

Multiply the combinations for each slot, also remembering that the number of choices decreases each time. 

n = total number of objects

r = number of permutations (slots)

n (n - 1)(n - 2)...x(n - r + 1) or n! / (n-r)!

Combinations: Single Source,

 Order Doesn't Matter

6 Horses(n)...How many different groups

of horses can make up the top 3(r)

First find the number of permutations based on what is asked. 

Then divide by the permutation of the number of choices/slots (r)

n(n-1)(n-2)...x(n-r+1) / r!