Find how many solutions there are to the given equation that satisfy the given condition. x1 + x2 + x3 = 22, each x; is a positive integer. need ? read it talk to a tutor

  210

Step-by-step explanation:

Consider 22 counters ("stars") placed in a row. There are 21 spaces between them. The problem here amounts to finding the number of ways that 2 separators ("bars") can be put in those spaces, dividing the row into 3 parts.

The number of ways 21 objects can be chosen 2 at a time is ...

  21C2 = 21!/(2!(21-2)!) = 21·20/(2·1) = 210

There are 210 positive integer solutions to the given equation.

Here are the first few solutions, to give you the idea:

  * | * | * * * ...   ⇒  (x1, x2, x3) = (1, 1, 20)

  * | * * | * * ...   ⇒  (x1, x2, x3) = (1, 2, 19)

  * | * * * | * ...   ⇒  (x1, x2, x3) = (1, 3, 18)

cheater

step-by-step explanation: