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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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