The AI Development Group has just recruited 8 math majors, 5 computer science majors, 3 physics majors, and 4 psychology majors. The company president would like to select three of them to join the Planning Department, but would like no two members to have the same major. How many choices does the president have?
Answer (2)
To solve this problem, we need to select three individuals where no two members have the same major. Let's look at the given options:
Math Majors : 8
Computer Science Majors : 5
Physics Majors : 3
Psychology Majors : 4
The requirement is to choose three individuals, each from a different major. We can achieve this by selecting one person from each of three different majors. There are several combinations of majors that can be chosen:
Math, Computer Science, Physics
Math, Computer Science, Psychology
Math, Physics, Psychology
Computer Science, Physics, Psychology
Next, we calculate the number of ways to select one person from each chosen set of majors:
Math, Computer Science, Physics : 8 (Math) × 5 (CS) × 3 (Physics) = 120
Math, Computer Science, Psychology : 8 × 5 × 4 = 160
Math, Physics, Psychology : 8 × 3 × 4 = 96
Computer Science, Physics, Psychology : 5 × 3 × 4 = 60
Finally, to find the total number of ways the president can select such a team, we add the number of combinations for each set:
120 + 160 + 96 + 60 = 436
Therefore, the president has 436 different ways to choose the three individuals, where no two members have the same major.
The president can select a team of three individuals from different majors in a total of 436 ways. To get this result, we consider the combinations of majors and calculate the selections for each combination. Adding these selections yields the total number of options available for the president.
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