10. Combinatorics & Probability

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $(5x\text{–}1{)}^3$

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

How many four-digit odd numbers less than 6000 can be formed using the digits 2, 4, 6, 7, 8, and 9?

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

Evaluate the given binomial coefficient. $\left(\frac{6}{6}\right)$

Find f(x + h) − f(x)/h and simplify. f(x) = x⁴+7

Write the first three terms in each binomial expansion, expressing the result in simplified form. (x² + 1)¹⁶

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (x²+2y)⁴

Use the formula for nPr to evaluate each expression. ₆P₆

Find the term indicated in each expansion. (x − 1)⁹; fifth term

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (2a + b)⁶

Find the term in the expansion of (x² + y²)⁵ containing x⁴ as a factor.

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $(3x+y{)}^3$

Use the formula for nCr to evaluate each expression. ₉C₅

Evaluate each expression.

$\frac{{}_4{C}_2{\cdot }_6{C}_1}{{}_{18}{C}_3}$