Module 3: Counting Rules

Question 1

what does with and without replacements mean?

Answer 1

replacement basically means repeats. with replacement is repeats allowed and without replacement is repeats allowed.

Question 2

what is the permutation eqn and when you do use it?

Answer 2

nPk = (n!)/(n-k)!

Use it when order matters and repeats are allowed

Question 3

what is the combination eqn and when do you use it?

Answer 3

(n!)/((k!)((n-k)!))

Use when order doesn’t matter and when repeats aren’t allowed

Question 4

what can you also call a combination?

Answer 4

binomial coefficient.

Question 5

what is the basic principle of coutning:

Answer 5

If r experiments that are to be performed are such that the first one may result in any of n1 possible outcomes;
and if, for each of these n1 possible outcomes, there are n2 possible outcomes of the second experiment; and if, for each of the possible outcomes of the first two experiments, there are n3 possible outcomes of the third experiment; and if . . ., then there is a total of possible outcomes of n1 * n2 * n3 * … * n_r the r experiments

Question 6

when would you use the basic principle of counting?

Answer 6

when order matters and with replacement

Question 7

what is the multinomial coeffiecent and when would you use it?

Answer 7

n!/(n_1! * n_2! * … * n_r!)

Without replacement, order doesn’t matter. Multiple more than 2 groups.