91Ó°ÊÓ

Expand the binomial by using Pascal's Triangle to determine the coefficients. $$(x+2 y)^{5}$$

Find the indicated term of the geometric sequence. $$\text { 3rd term: } a_{1}=16, a_{4}=\frac{27}{4}$$

The deck for a card game is made up of 108 cards. Twenty-five each are red, yellow, blue, and green, and eight are wild cards. Each player is randomly dealt a seven-card hand. (a) What is the probability that a hand will contain exactly two wild cards? (b) What is the probability that a hand will contain two wild cards, two red cards, and three blue cards?

Find the indicated term of the geometric sequence. $$\text { 1st term: } a_{2}=3, a_{5}=\frac{3}{64}$$

Expand the binomial by using Pascal's Triangle to determine the coefficients. $$(3 v+2)^{6}$$

The first two terms of the arithmetic sequence are given. Find the missing term. $$a_{1}=3, a_{2}=13, a_{9}=$$

Write an expression for the apparent \(n\) th term \(\left(a_{n}\right)\) of the sequence. (Assume that \(n\) begins with 1.) $$1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}, \frac{1}{120}, \ldots$$

Find the number of distinguishable permutations of the group of letters. \(\mathbf{B}, \mathbf{B}, \mathbf{B}, \mathbf{T}, \mathbf{T}, \mathbf{T}, \mathbf{T}, \mathbf{T}\)

Use mathematical induction to find a formula for the sum of the first \(n\) terms of the sequence. $$\frac{1}{2 \cdot 3}, \frac{1}{3 \cdot 4}, \frac{1}{4 \cdot 5}, \frac{1}{5 \cdot 6}, \ldots, \frac{1}{(n+1)(n+2)}, \dots$$

Find the number of distinguishable permutations of the group of letters. \(\mathbf{A}, \mathbf{L}, \mathbf{G}, \mathbf{E}, \mathbf{B}, \mathbf{R}, \mathbf{A}\)