Question

Given 16 subjects from which to choose, in how many ways can a student select fields of study as follows? A major and a minor

Answer 1

To determine the number of ways a student can select a major and a minor from 16 subjects, we can use the concept of combinations.

The number of ways to choose a major from 16 subjects is 16, as the student can select any one of the 16 subjects as their major.

For the minor, since the student has already chosen a major, they have 15 remaining subjects to choose from. Therefore, the number of ways to choose a minor is 15.

To find the total number of ways to select a major and a minor, we multiply the number of choices for each category:

Total number of ways = Number of ways to choose a major × Number of ways to choose a minor
= 16 × 15
= 240

Therefore, a student can select a major and a minor from 16 subjects in 240 different ways.

Answer 2

A student can select a major and a minor from 16 subjects in 120 different ways.

Step-by-step explanation:

In order to calculate the number of ways a student can select a major and a minor from 16 subjects, we can use the concept of combinations. Since order does not matter, we can use the formula for combinations, which is nCr = n! / (r!(n-r)!), where n is the total number of subjects and r is the number of subjects to be selected.

For this question, we want to select one major and one minor. Therefore, n = 16 and r = 2. Plugging these values into the formula, we get 16C2 = 16! / (2!(16-2)!) = 120 ways.

So, a student can select a major and a minor from 16 subjects in 120 different ways.