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1.10 friends are at a party and they decided the party was boring and decided to go to a
club in two different cars. One of the friends, Susan, has an SUV that can carry 7
passengers. So, Susan can take 6 more of the 9 friends with her. How many
different groups of 6 people are possible from the 9 remaining friends?

Sagot :

Using the combination formula, it is found that 84 different groups of 6 people are possible from the 9 remaining friends.

The order in which the friends are chosen is not important, hence the combination formula is used to solve this question.

What is the 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, 6 friends are chosen from a set of 9, hence:

[tex]C_{9,6} = \frac{9!}{6!3!} = 84[/tex]

84 different groups of 6 people are possible from the 9 remaining friends.

More can be learned about the combination formula at https://brainly.com/question/25821700