10. Combinatorics & Probability

Evaluate each expression.

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

Find the middle term in the expansion of (3/x + x/3)¹⁰

Use the formula for _nP_r to evaluate each expression. ₈P₅

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

Find the term indicated in each expansion. (2x + y)⁶; third term

Write the first three terms in each binomial expansion, expressing the result in simplified form. (y³ − 1)²⁰

Use the formula for nCr to evaluate each expression. ₇C₇

Use the formula for nCr to solve Exercises 49–56. To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?

Find the term indicated in each expansion. (x² + y)²²; the term containing y¹⁴

Use the formula for nCr to evaluate each expression. ₁₀C₆

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

Use the formula for nCr to solve Exercises 49–56. An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

Write the first three terms in the binomial expansion, expressing the result in simplified form. (x-3)^9

Use the Binomial Theorem to expand each expression and write the result in simplified form. (x³ +x^-2)⁴

Use the formula for nCr to solve Exercises 49–56. You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?