How many solutions are there for the equation x + y + z = 8 for which a) x, y, and z are all positive? b) x, y, and z are all non-negative?

a). There are 21 positive solutions    and    b). There are 45 solutions.

Step-by-step explanation:

Given:

Equation, x + y + x = 8

To find: a).  x, y, and z are all positive

             b). x, y, and z are all non-negative

Here, Finding the number of solutions is equivalent to finding the number of ways to distribute 8 objects among 3 places.

a).

First let us given each place 1 object each.

Now, we find the number of ways to distribute 5 objects among three places.

Number of ways =

⇒ There are 21 positive solutions

b).

Here, we find the number of ways to distribute 8 objects among three places.

Number of ways =

⇒ There are 45 negative solutions.

Therefore, a). There are 21 positive solutions    and    b). There are 45 solutions.

on your paper it doesn't say the answer but the the answer is altitude

step-by-step explanation: