10. Combinatorics & Probability

You want to arrange the books on your bookshelf by color. How many different ways could you arrange 12 books if 4 of them have a blue cover, 3 are yellow, and 5 are white?

How many options are there for license plates with any three letters (A-Z) followed by any 3 numbers (0-9)?

How many possible outcomes are there if you roll 5 dice?

Phone numbers are 10 digits long. How many possible phone numbers are there if the 1^st and 4^th numbers can't be 0?

Emily is organizing her closet. She has 15 shirts left to hang but has space in one section for 6 shirts. How many ways could she hang shirts in that section?

How many ways are there to arrange the letters in the word CALCULUS?

Evaluate the given expression. ${}_9{P}_4$

A student formed a club at their school. They have 13 members, and need to elect a president, vice president, and treasurer. How many ways are there to fill these officer positions?

Evaluate the given expression. ${}_{11}{C}_7$

From a class of 28 students, in how many ways could a teacher select 4 students to lead the class discussion?