Question

A student can take one of four Mathematics sections
and one of five English sections. The number n of ways
he can register for the two courses, is​

Answer 1

s we are currently learning Permutations and Combinations, my above interpretation is that it is asking for a Combination without repetition or (n+r−1)!r!(n−1)! which gives you the amount of combinations without repetition (as you cannot pick the same student twice.) Now my teacher argues that the answer the book provides is correct. The books answer simply says to use nCr or n!r!(n−r)!.

What is the correct method of answering this? The book states 3. 495 is the answer.n:

Answer 2

The number of ways a student can register for Mathematics and English sections can be found by using the multiplication principle.

According to the multiplication principle, the total number of ways to perform a sequence of tasks is the product of the number of ways each task can be performed.

Therefore, the number of ways a student can register for Mathematics and English sections is:

n = number of ways to select a Mathematics section * number of ways to select an English section

Since the student can select one of four Mathematics sections and one of five English sections, we have:

n = 4 * 5 = 20

Therefore, the student can register for the two courses in 20 different ways.

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