3. Suppose a bookcase shelf has 5 Mathematics texts, 3 Biology texts, 6 Chemistry texts and 4 Physics texts. Find the number n of ways a student can choose:
a. one of the texts;
b. one of each type of text.
a. To find the number of ways a student can choose one of the texts, we simply need to add up the number of texts in each subject:
Number of Mathematics texts = 5
Number of Biology texts = 3
Number of Chemistry texts = 6
Number of Physics texts = 4
Therefore, the total number of texts is:
Total texts = Number of Mathematics texts + Number of Biology texts + Number of Chemistry texts + Number of Physics texts
= 5 + 3 + 6 + 4
= 18
So, there are 18 different texts a student can choose from.
b. To find the number of ways a student can choose one of each type of text, we need to consider the product of the number of choices in each subject:
Number of choices for Mathematics text = 5
Number of choices for Biology text = 3
Number of choices for Chemistry text = 6
Number of choices for Physics text = 4
Therefore, the total number of ways to choose one of each type of text is:
Total ways = Number of choices for Mathematics text × Number of choices for Biology text × Number of choices for Chemistry text × Number of choices for Physics text
= 5 × 3 × 6 × 4
= 360
So, there are 360 different ways a student can choose one text from each type.