Permutations & Combinations (DP IB Analysis & Approaches (AA))

Counting principles are methods used to determine the number of possible outcomes in various situations.

AND typically indicates that values should be multiplied in counting problems.

E.g. if you are choosing a pen and a pencil from 4 pens and 5 pencils, there are 4×5=20 possible ways of choosing.

OR typically indicates that values should be added in counting problems.

E.g. if you are choosing a pen or a pencil from 4 pens and 5 pencils, there are 4+5=9 possible ways of choosing.

When choosing 1 item from a list of m items AND 1 item from a list of n items there are m×n possible combinations.

This can be thought of as the fundamental counting principle.

False.

When selecting a 4-digit PIN number, the number of possibilities is smaller if every digit has to be a different number.

If each digit can be any number ('with replacement') there are possible PIN numbers.

If each digit must be different ('without replacement') there are only possible PIN numbers.

The key difference between permutations and combinations is that order matters in permutations but not in combinations.

E.g. ACE, AEC, CAE, CEA, EAC and ECA are six separate permutations of those three letters. But those would only count as one combination of three letters.

n! (n factorial) is the product of all positive integers less than or equal to n.

I.e.

False.

0! equals 1.

There are n! possible permutations of n different objects.

If you arrange r out of n different objects, there are  possible permutations.

This formula is in your exam formula booklet. However you will usually use the function on your GDC to calculate this, rather than using the formula.