Calculating Unique Combinations for Notebooks and Pens

Question:

Why is the man able to try 72 unique combinations by selecting one notebook and one pen each day?

Answer:

The man is able to try 72 unique combinations because he has 4 notebooks and 3 pens to choose from. To calculate the number of unique combinations, we can use the formula for combinations which is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items chosen at a time.

Explanation:

Step 1: The man is choosing 1 notebook from 4 options. Therefore, the number of combinations for notebooks is 4C1.

Step 2: The man is choosing 1 pen from 3 options. Hence, the number of combinations for pens is 3C1.

By applying the formula for combinations, we can calculate the total number of unique combinations:

Number of combinations = 4C1 * 3C1

= (4! / (1!(4-1)!)) * (3! / (1!(3-1)!))

= (4 * 3) * (3 * 2)

= 12 * 6

= 72

Therefore, the man can try 72 unique combinations by selecting one notebook and one pen each day.