Permutations and Combinations-Single Row, Multiple Row Problems

I am studying perms and combs on my own for a course which i want to take in the future. I have come across 2 questions, to which I need a solution. I would also need the reasoning applied to the solution for future application. Here are the 2 questions.

Question 1. How many ways can 18 different vehicles be arranged in a car dealership showroom?
a) In a single row ?
b) In 2 rows, where 7 of the vehicles are trucks to be arranged in one row, and the other 11 vehicles are cars, to be arranged in another row?

Question 2. There are 18 people in a choir, for a school of music. How many different ways can they be arranged.
a) In a single row?
b) In 3 rows, with 5 in the first row, 6 in the second row, and 7 in the third row ?

Thank You . Please make sure to include the reasoning for the answer, so that I can apply to future problems.

Solution Preview

Question 1. How many ways can 18 different vehicles be arranged in a car dealership showroom?

a) In a single row ?

This is a straight permutation of 18 items, so use the factorial 18! = 18x17x16 ....x3x2x1. This is a very large number over 6400 ...

Solution Summary

The expert examines permutations and combinations and sing and multiple row problems.

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a) The boys and gir

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1. Find the dot product for the following pairs of vectors:
a. Row vector = (2 0) Column vector is below
5
18
b. Row vector = (3 9 -4) Column vector is below
3
0
2
c. Row vector = (5 6 7 8)
1
1
1
1
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0 -2 5
A= 3 -4 17
1 2 3
9 7 2
-3

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Eq 1: x + y = 2
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I set up my matricies in the following:
1 1 0 2
0 1 1 3
1 2 1 5
operation 1: (-1*row 1 +row 3)
1 1 0 2
0 1 1 3
0 1 1 3
operation 2: (-1*row 2 +row 3)
1 1 0 2
0 1 1 3
0 0

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Enter row 1: 8 3 9 0 10
Enter row 2: 3 5 17 1 1
Enter row 3: 2 8 6 23 1
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Row Totals:
Column Totals:
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