Question

The number of triplets of x,y,z, where x,y,z are distinct non-negative integers satisfying xyz=15 is:

a. Not provided.
b. Calculate based on given data.
c. Data missing.
d. None of the above.

Answer 1

To find the number of distinct triplets of non-negative integers (x, y, z) such that xyz = 15, we factorize 15 and consider the limited number of its factors, resulting in 6 possible triplets.

Step-by-step explanation:

The question asks for the number of triplets of x,y,z, which are distinct non-negative integers such that xyz = 15. Here's how to calculate:

Step 1: Factorize the number 15

15 can be factorized into 3x5. Since we need three distinct numbers, one must be 1 to satisfy the quotient of 15, given the limited factors.

Step 2: Find the triplets

The triplets that satisfy the condition are derived from the factors of 15, considering that at least one of the numbers has to be 1. The possible triplets are:

• (1, 3, 5)
• (1, 5, 3)
• (3, 1, 5)
• (3, 5, 1)
• (5, 1, 3)
• (5, 3, 1)

Therefore, there are 6 distinct triplets where x, y, and z are distinct non-negative integers that satisfy xyz = 15.

Answer 2

To find the number of triplets satisfying the equation xyz = 15, we can find all the distinct combinations of x, y, and z that satisfy the equation.

Step-by-step explanation:

Given the equation xyz = 15, we need to find the number of triplets (x, y, z) where x, y, and z are distinct non-negative integers.

To solve this problem, we need to find all the possible combinations of x, y, and z that satisfy the equation.

Here are the distinct triplets that satisfy the equation: (2, 3, 2), (1, 5, 0), (3, 1, 5), and (5, 1, 3). So, there are a total of 4 triplets that satisfy the equation.