Q. Find the odd positive integer of the number 4380.

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Q. For a gaming competition, 8 girls are planning on splitting up into 3 (non-empty) groups. How many ways can they split up into these groups?

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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?

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

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

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

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

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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?

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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.

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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.

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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?

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

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

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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.

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

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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.

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

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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.

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

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

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