A group of 20 friends are going to travel to a school reunion together, 7 of them can drive. They have a 7 seat car (1 driver and 6 passengers), a 5 seat car (1 driver and 4 passengers) and the remaining 8 will take a bus. How many ways can the friends travel (ignoring passenger seat positions within each vehicle)? Give an exact answer, do not round. Do not include commas or dots in your answer.

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21-10-2021
Mathematics

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A group of 20 friends are going to travel to a school reunion together, 7 of them can drive. They have a 7 seat car (1 driver and 6 passengers), a 5 seat car (1 driver and 4 passengers) and the remaining 8 will take a bus. How many ways can the friends travel (ignoring passenger seat positions within each vehicle)? Give an exact answer, do not round. Do not include commas or dots in your answer.

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joaobezerra joaobezerra · Answer 1 · 2021-11-03T09:25:37+01:00

Using the combination formula, it is found that there are 99768240 ways in which they can travel.

The passenger seat positions are not important, which means that the order is not important, which is why the combination formula is used.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem:

In the first car, 7 of the 20 friends are going to sit.
In the second, 5 of the remaining 13 are going to sit.
In the bus, the remaining 8.

The, the number of ways is given by:

[tex]N = C_{20,7}C_{13,5}C_{8,8}[/tex]

[tex]N = \frac{20!}{7!13!} \times \frac{13!}{5!8!} \times \frac{8!}{0!8!} = 99768240[/tex]

There are 99768240 ways in which they can travel.

A similar problem is given at https://brainly.com/question/24437717