VA group of 40 students from your school is part of the audience for a TV game show. The total number of people in the audience is 130. What is the theoretical probability of 5 students from your school being selected as contestants out of 9 possible contestant spots?

0.76%

Step-by-step explanation:

This exercise is solved through combinations.

The first is the number of combinations of students that would go in that course, that is, 5 out of 40.

Formula: nCx = n! / X! * (N-x) !

40C5 = 40! / [5! * (40 - 5) !] = 658008

Also the number of combinations of the other members of the audience that occupy the other 4 places (9 in total - 5 of the group), that is 4 of 90 (130 total - 40 of the group658008po).

90C4 = 90! / [4! * (90 - 4) !] = 2555190

The total of possible combinations 9 contestants with 5 students in them, would be:

40C5 * 90C4

Now, the total number of possible 9 contestants from the audience would be 9 in 130:

130C9 = 130! / [9! * (130 - 9) ! = 2.2016 * 10 ^ 13

The probability would be equal to:

40C5 * 90C4 / 130C9 = 658008 * 2555190 / (2.2016 * 10 ^ 13) = 0.076

In other words, the probability is 0.76%