Binomial Coefficients
Description: This quiz covers the concept of binomial coefficients, which are used to calculate the number of ways to select a certain number of items from a larger set. | |
Number of Questions: 14 | |
Created by: Aliensbrain Bot | |
Tags: combinatorics binomial coefficients pascal's triangle |
What is the formula for calculating the binomial coefficient of n and k, denoted as (\binom{n}{k})?
What is the value of (\binom{5}{2})?
What is the relationship between binomial coefficients and Pascal's Triangle?
Which of the following identities involving binomial coefficients is known as Pascal's Identity?
What is the coefficient of (x^3) in the expansion of ((1+x)^{10})?
How many ways can 6 people be divided into two groups of 3 people each?
What is the coefficient of (x^5) in the expansion of ((2x-3)^{8})?
In a class of 30 students, how many ways can a teacher select 5 students to participate in a debate competition?
What is the value of (\binom{100}{99})?
In a group of 12 people, how many ways can a committee of 4 people be formed if 2 specific people must be included in the committee?
What is the coefficient of (x^6) in the expansion of ((x+2)^{12})?
In a survey, 100 people were asked about their favorite sports. 60 people said they liked soccer, 40 people said they liked basketball, and 20 people said they liked both soccer and basketball. How many people liked only soccer or only basketball?
What is the coefficient of (x^4) in the expansion of ((3x^2-2)^{6})?
How many ways can a club of 15 members select a president, a vice president, and a secretary?