Combinations and Permutations: Cribbage Word Problem

In the game of cribbage, as long as one card is different, you can score points. Two of a kind, like a pair of aces, is worth 2 points. How many points are made using 4 of a kind?

Simplifying permutations.

What is the value of P(23,17)?

Permutation: Factorial

Permutation 89! __________ 80!(89-80)!

Word problem in regards to arithmetic sums.

The game of pool uses 15 balls numbered 1 to 15. In a variety called rotations, a player who sinks a ball receives as many points as the number on the ball. What is the score of a player who sinks all 15 balls?

Word problem in regards to geometric sequences.

A college student humorously asks his parents to charge him room and board according to this geometric sequence: $0.01 for the first day of the month, $0.02 for the second day, $0.04 on the third day and so on. Find the total room and board he would pay for 30 days.

Working with binomial expansion.

Find the fourth term of this expansion: (3x-4y)^11

Writing fractions with the same denominator

Write (x+4)/(x^2-3x-10) and 2x/(25-x^2) with the same denominator.

Factoring a Polynomial

Factor: -2x^3 - 16x^2 + 40x

Using Cramer's Rule with a 3x3 System

Using Cramer's Rule with a 3x3 system 3x+4y+z=17 2x+3y+2z=15 x+y =4

Solving for a variable in a quadratic fraction polynomial.

Solve for x: 6/(x^2-7x+6)=2/(x-1)-4/(x-6)