10. Combinatorics & Probability

Use the formula for nCr to evaluate each expression. ₁₁C₄

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (c+2)⁵

Use the formula for nPr to evaluate each expression. ₈P₀

A club with 15 members is to choose four officers–president, vice president, secretary, and treasurer. In how many ways can these offices be filled?

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

Use the Binomial Theorem to expand and then simplify the result: (x² +x+ 1)³.

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $(2x+1{)}^4$

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

Evaluate the expression. *permutation notation* the number of permutations 9 things taken 5 at a time (sub 9)P(sub 5)

Evaluate the given binomial coefficient 11 8

Write the first three terms in each binomial expansion, expressing the result in simplified form. (x+2)⁸

How many different ways can a director select 4 actors from a group of 20 actors to attend a workshop on performing in rock musicals?

Evaluate each expression.

$\frac{{}_7{P}_3}{3!}{-}_7{C}_3$

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (3x − y)⁵

Evaluate the given binomial coefficient.$\left(\frac{8}{3}\right)$