Daily Problems

Answers, explainations and code for each of the daily problems on my youtube channel

Click here to see the prerequisits for most of these puzzles

Things you should be familiar with before attempting these problems

Addition Rule: Count number of ways that mutually exclusive events can happen.

Expample: How many ways can I order one of $3$ sandwiches or one of $2$ soups? $3+2$

Product Rule: Count number of ways the simultainious events can happen

Example: How many ways can I order one of $3$ sandwiches and one of $2$ soups? $3 \cdot 2$

Inclusion-Exclusion principle: Subtract elements that have been counted multiple times.

Example: How many ways can a die land on an odd number or a number less than $3$? $3 + 2 - 1$

Factoials: $n!$

Example: $5! = 5 \cdot 4 \cdot 3 \cdot 2$

Permutations: ${}^{n}{P}_r$

Example: $\prescript{5}{}{P}_3 = 5 \cdot 4 \cdot 3 = \dfrac{5!}{(5-3-1)!}$

Binomial Theorem: ${ n \choose r }$

Example: ${ 5 \choose 3} = \dfrac{5!}{(5-3-1)! \cdot 3!}$

Sigma notation: $$\sum_{i=1}^{n}i$$

Example: $$\sum_{i=1}^{5} i = 1 + 2 + 3 + 4 + 5 = 15$$