A student science club consists of 20 biology majors, 13 chemistry majors, and 8 physics majors. One student from each of the three sciences is to be selected to participate in a special project. How many different ways can these three students be selected?How many ways can the club select a president,vice president, and a treasurer?
A certain committee consists of 5 people. From the committee, a president, a vice-president, and a secretary are to be chosen. In how many ways can these 3 offices be filled? Assume that a committee member can hold at most one of these offices.
To find the number of different ways to select three students from the science club, we can use the product rule of counting.
Step 1: Calculate the number of ways to select one biology major.
Since there are 20 biology majors, we have 20 choices for the first selection.
Step 2: Calculate the number of ways to select one chemistry major.
Since there are 13 chemistry majors remaining, we have 13 choices for the second selection.
Step 3: Calculate the number of ways to select one physics major.
Since there are 8 physics majors remaining, we have 8 choices for the third selection.
Using the product rule, we multiply the number of choices at each step: 20 * 13 * 8 = 2,080.
Therefore, there are 2,080 different ways to select three students from the science club.
Now, let's move on to the second part of the question - the selection of a president, vice president, and treasurer.
Step 1: Calculate the number of ways to select a president.
Since there are 41 students in total (20 biology majors, 13 chemistry majors, and 8 physics majors), we have 41 choices for the first position.
Step 2: Calculate the number of ways to select a vice president.
Since we have already selected one student for the president position, there are 40 remaining students. Therefore, we have 40 choices for the second position.
Step 3: Calculate the number of ways to select a treasurer.
Since we have already selected two students, there are 39 remaining students. Therefore, we have 39 choices for the third position.
Using the product rule again, we multiply the number of choices at each step: 41 * 40 * 39 = 63,240.
Therefore, there are 63,240 different ways to select a president, vice president, and treasurer from the science club.