Question

A school has 5 spanish teachers and 4 French teachers. The school's principal randomly chooses 2 of the teachers to attend a conference. What is the probability that the principal chooses 2 spanish teachers?

Answer 1

To find the probability of choosing 2 Spanish teachers from a group of 9 teachers, we calculate the total number of combinations of 2 teachers and the number of combinations of 2 Spanish teachers. Then, we divide the latter by the former to find the probability.

Step-by-step explanation:

To find the probability that the principal chooses 2 Spanish teachers, we need to determine the total number of possible combinations to choose 2 teachers out of the 9 total teachers and the number of combinations that consist of only Spanish teachers.

The total number of combinations to choose 2 teachers out of 9 is given by the formula C(9, 2), which is calculated as 9! / (2! * (9 - 2)!), where ! denotes factorial. This simplifies to 9! / (2! * 7!).

The number of combinations that consist of only Spanish teachers is given by the formula C(5, 2), which is calculated as 5! / (2! * (5 - 2)!), where 5 is the number of Spanish teachers. This simplifies to 5! / (2! * 3!).

Finally, the probability is calculated by dividing the number of combinations of only Spanish teachers by the total number of combinations.

Therefore, the probability that the principal chooses 2 Spanish teachers is C(5, 2) / C(9, 2).