Q. In a picnic with 20 persons where 6 chocolates will be given to the top 8 children(the chocolates are distinct: first, second). How many ways can this be done?

View solution

Q. How many ways can one choose 20 cookies from 45 different types (assuming there are at least 20 of each type)?

View solution

Q. Assume that it is an afternoon. What is the time on the 24 hour clock after 146 hours?

View solution

Q. There are 28 identical oranges that are to be distributed among 8 distinct girls. How many ways are there to distribute the oranges?

View solution

Q. There are 5 distinct fruits. How many ways can they be planted into identical fruit plants?

View solution

Q. A woman has 14 identical pens to distribute among a group of 10 distinct students. How many ways are there to distribute the 14 pens such that each student gets at least one pencil?

View solution

Q. Suppose that M is the product of k distinct primes. Find the number of ways to write N as the product of positive integers(>1), where the order of terms does not matter.

View solution

Q. How many ways are there to place 7 differently colored toys into 5 identical urns if the urns can be empty? Note that all balls have to be used.

View solution

Q. Suppose, there are 7 of your friends who want to eat pizza (8 distinct people in total). You order a 16-cut pizza (16 identical slices). How many distributions of pizza slices are there if each person gets at least one slice of pizza?

View solution

Q. The linear system Cx = d is known as _________ if d! = 0.

View solution

Q. Every linear equation determines a _______ in n-dimensional space for n variables.

View solution

Q. Determine all possibilities for the number of solutions of the system of 7 equations in 5 unknowns and it has x₁ = 0, x₂ = −6, and x₃ = 4 as a solution.

View solution

Q. Determine all possibilities for the solution set of the homogeneous system that has y₁ = 6, y₂ = −4, y₃ = 0 as a solution.

View solution

Q. Determine all possibilities for the solution set of the homogeneous system of 5 equations in 3 unknowns and the rank of the system is 3.

View solution

Q. Determine all possibilities for the solution set of a homogeneous system that has y₁ = 5, y₂ = −3, y₃ = 2 as a solution.

View solution

Q. Determine all possibilities for the solution set of the system of 2 equations in 3 unknowns that has x₁ = 4, x₂ = −7, x₃ = 0 as a solution.

View solution

Q. Determine all possibilities for the solution set of a homogeneous system of 4 equations in 4 unknowns.

View solution

Q. Determine all possibilities for the solution set of a homogeneous system of 6 equations in 5 unknowns.

View solution

Q. Determine all possibilities for the solution set of a homogeneous system of 5 equations in 4 unknowns and the rank of the system is 3.

View solution

Q. Determine the number of derangements of (2, 4, 6, 1, 3, 5) that end with integer 2, 4 and 6 in some order?

View solution