1. Miscellaneous Tricks Letter Permutations Equations Quick Arithmetic

2. Letter Permutations Take number of letters factorial. Divide by the factorial of each amount of repeated letters. Ex. LOL: 3 letters total, L repeated twice. 3!/2!=3 Ex. LOLOL: 5 letters total, L repeated three times, O repeated twice 5!/(3!*2!)=10

3. Equations You need not always find actual values for variables. Ex. ab=5, ab^2=7, abc=2. What is b-c? ab^2-abc=7-2=5. ab(b-c)=5; 5(b-c)=5 b-c=5 It is usually possible to multiply and add what you have to end up with what you need, instead of going to the values of the variables.

4. Quick Arithmetic Simplify Fractions. Ex. 12 choose 6. (12*11*10*9*8*7)/(1*2*3*4*5*6) (12*11*10*9*7)/(3*5*6) (12*11*10*7)/(5*2) (6*11*2*7)=66*7*2=462*2=924.

5. Quick Arithmetic (a+b)(a-b) = a^2-b^2 Ex. 15*25 (20-5)(20+5) 20^2-5^2 400-25 = 375 (a+b)^2= a^2 + 2ab +b^2. (a-b)^2= a^2 - 2ab +b^2. Ex. 98^2 (90+8)^2 8100+2*90*8+64 8100+1440+64=9604

6. Probability Trees One method to find desired and possible, like organized counting. Ex. You can put on a red, blue or yellow sock. You have a pair of tennis shoes, slippers, and soccer cleats. You are willing to wear any of these shoes with the red or blue socks, but you won’t wear slippers and yellow socks. What is the probability that you wear tennis shoes?