Final answer:
There are 3,654 ways to select 4 leaders including Natasha from a class of 30 students. The probability of Natasha being one of the leaders is approximately 13.33%.
Step-by-step explanation:
If Natasha must be one of the 4 leaders chosen from a class of 30 students, we first recognize that one leader position is already taken by Natasha, leaving us with 3 leader positions to fill from the remaining 29 students.Now, the number of ways to select the 3 remaining leaders from 29 students is a combination problem, which is given by the formula C(n, k) = n! / (k!(n - k)!), where 'n' is the total number of options and 'k' is the number of choices to make. In this case, it's C(29, 3).The calculation is: C(29, 3) = 29! / (3! * (29 - 3)!) = 29! / (3! * 26!) = 3654 ways.
The probability that any specific combination of 4 leaders including Natasha will be chosen is 1 in C(30, 4), because there is only one way to choose Natasha and a specific set of 3 others. C(30, 4) gives us the total number of ways to select 4 leaders from 30 students without any restrictions.This probability calculation would typically use the formula for combinations as well, yielding C(30, 4) = 30! / (4! * (30 - 4)!) = 27,405 total combinations. Therefore, the probability of choosing a group that includes Natasha is 3654/27405, which simplifies to approximately 0.1333 or 13.33%.