skylarhinson
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125 students have volunteered to be on the prom committee. 2 of those students will be randomly chosen to win free tickets to the prom. How many different ways can the winners be chosen?


Does order matter? Answer

No

This is a Answer

combination

.

How many different ways can winners be chosen?

Answer

125

Answer

C

Answer

2

= Answer

7750

What is the probability that the first two students who signed up will be the winners? P(1st two students who signed up win) = Answer



Answer :

Using the combination formula, it is found that:

  • There are 7750 different ways for the winners to be chosen.
  • The probability that the first two students who signed up will be the winners is 1/7750.

The order in which the students are chosen is not important, as for example, João and Elisa is the same outcome as Elisa and João, 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 the following formula, involving factorials.

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

2 students are chosen from a set of 125, hence the number of combinations is:

[tex]C_{125,2} = \frac{125!}{2!123!} = 7750[/tex]

There are 7750 different ways for the winners to be chosen.

The first two students winning is only one outcome, hence:

The probability that the first two students who signed up will be the winners is 1/7750.

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

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