10. Combinatorics & Probability

Evaluate each expression.

$\frac{{}_7{C}_3}{{}_5{C}_4}-\frac{98!}{96!}$

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (x+2)³

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (x − 1)⁵

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

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

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?

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?

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?

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

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

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

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

Find the term indicated in each expansion. (x − 1/2)⁹; fourth term

Find the term indicated in each expansion. (x² + y³)⁸; sixth term