Five college engineering students are choosing specialized fileds of engineering to study. Each student is allowed to select 1 field. The available fields are Electrical Engineering (EE), Mechanical Engineering (ME), and Computer Engineering (CE). If the second student does not meet the requiremets for ME and the third student does not meet the requirements for CE then how many ways are there for the students to choose an engineering field? Assume that there are 10 slots available for each of the three fields and different students are allowed to choose the same field.
The pie chart below shows how the annual budget for a certain company is divided by department. If the amount budgeted for Research and Engineering combined is , what is the total annual budget?
To solve this problem, we'll use the concept of permutations.
Let's analyze the given information step by step:
1. The total number of students is 5.
2. Each student can choose a specialized field from three available options: EE, ME, and CE.
3. The second student does not meet the requirements for ME, and the third student does not meet the requirements for CE.
Using these conditions, we need to determine the number of ways the students can choose their engineering fields.
First, let's calculate the number of ways the second student can choose a field:
Since the second student cannot choose ME, there are two available options for them (EE and CE). Therefore, the second student has a choice of 2 fields.
Next, let's calculate the number of ways the third student can choose a field:
Since the third student cannot choose CE, there are two available options for them (EE and ME). Therefore, the third student has a choice of 2 fields.
Now, for the remaining students (students 1, 4, and 5), they can choose from all three available fields (EE, ME, and CE). Thus, for each of these three students, there are three available options.
Multiplying the choices for each student will give us the total number of ways 5 students can choose their engineering fields:
Total number of ways = (Choices for student 1) x (Choices for student 2) x (Choices for student 3) x (Choices for student 4) x (Choices for student 5)
Total number of ways = 3 x 2 x 2 x 3 x 3
Total number of ways = 108
Therefore, there are 108 different ways for the five college engineering students to choose their specialized fields.