10. Combinatorics & Probability

Evaluate each expression.

$1-\frac{{}_3{P}_2}{{}_4{P}_3}$

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (2x³ − 1)⁴

Use the Binomial Theorem to expand the binomial and express the result in simplified form. ((x^2)-1)^4

Evaluate n!/(n-r)! for n = 20 and r = 3

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?

Write the first three terms in each binomial expansion, expressing the result in simplified form. (x - 2y)¹⁰

Use the Fundamental Counting Principle to solve Exercises 29–40. An ice cream store sells two drinks (sodas or milk shakes) in four sizes (small, medium, large, or jumbo) and five flavors (vanilla, strawberry, chocolate, coffee, or pistachio). In how many ways can a customer order a drink?

Use the formula for _nP_r to evaluate each expression. ₁₀P₄

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

Evaluate the given binomial coefficient. $\left(\frac{100}{2}\right)$

Use the Fundamental Counting Principle to solve Exercises 29–40. A popular brand of pen is available in three colors (red, green, or blue) and four writing tips (bold, medium, fine, or micro). How many different choices of pens do you have with this brand?

Use the Binomial Theorem to expand the binomial and express the result in simplified form. (2x+1)^3

Use the formula for _nP_r to evaluate each expression. ₉P₄

Use the Binomial Theorem to expand each expression and write the result in simplified form. (x^1/3 +x^-1/3)³

In how many ways can five airplanes line up for departure on a runway?