CISC 102 - Day 7

2024-10-02 16:29:15 -0400 EDT


Product Rule

You got two tasks. the first task has $n_1$ solutions, the second task has $n_2$ solutions. Then the total amount of solutions between them is $n_1n_2$

Sum Rule

You got two tasks. the first task has $n_1$ solutions, the second task has $n_2$ solutions. Then the total amount of solutions between them is $n_1 + n_2$

Definition: Permutations are a set of distinct objects in a ordered arrangement such that

$P(n, r) = \frac{n!}{(n - r)!}$

r = permutations n = amount of solutions P = amount of permutations

Note: $n! = n(n - 1)(n - 2 ) … (1)$


Definition: r-combination of elements of a set is an unordered subset of the given set denoted by $C(n, r)$ such that

$C(n, r) = n! \ r! (n -r)!$

Note: $C(n, r) = C(n, n - r)