Planet 3 Flashcards
Specific questions…
Ways to efficiently find answers after first initial read.
Specific questions…
Always return back to the passage
Initial read…
Don’t worry about understanding details in initial read. Know where things are so you can come back and find them
3! and 4! are examples of a…
Factorial
General permutations…
Ordered arrangement of elements without repititions. Use basic counting principles. N! (Letters in a password without repition)
Permutations with repeating elements…
Permutations of elements, some of which are indistinguishable of others. To arrange N items (of which some repeat)… N! / A!B!C! where A B and C represent the number of times the unique items appear
How many times can 3 quarters, 2 nickels and 1 dime be arranged, all heads up, in a row…
6! / 3!2!1!
Combinations…
Unordered arrangement of elements. Ex - members in a committee or students in a study group
Combinations formula
N! / In!Out!
Combinations v Permutations
Combinations are unordered, permutations are ordered
General permutations…
Generally easiest to think through them and solve using the “slotting method”
Slotting method
Used in permutations. Determine how many arrangments are available in each slot, and multiply
Dealing with restrictions…
1) Solve unrestrained and then subtract number of constraints or 2) Account for restraint up front and calculate the number of possibilities around the contraints
Solving unrestrained and then subtracting example…
With combinations and restrictions, you can easily account for the constraint by making it happen and subtracting from the total. Example: How many 4-person teams can be chosen from a group of 6 people if Katy and Taylor refuse to be on the same team? The number of total options (pre-constraint) is 6!/4!2!=15. To subtract the constraint, put Katy and Taylor on the team, leaving 4 people left for 2 spots: 4!/2!2!=6, so the answer is 15 – 6 = 9.
Problems with multiple comb/perm problems…
And = multiply; or = add
