How many different integer solutions are there to the equati

How many different integer solutions are there to the equation

x1 + x2 + x3 + x4 = 21

0 xi 9?

Solution

Given x1+x2+x3+x4=21, ....0=<xi=<9

Here given that different integer solutions that mean in one solution the elements may not be equal to other element (same number is not repeated in the same solution)here frist we have to note that

For same numbers we have[0,4,8,9],(0,6,7,8),(0,5,7,9)(1,3,8,9)(1,4,7,9)(1,5,7,8)(1,5,6,9)(2,3,7,9)(2,4,6,9)(2,5,6,8)((2,4,7,8)(3,5,4,9)(3,4,6,8)(3,5,6,7)....so without repeating the values we get these....

But here the values don\'t be same but they may interchange

Hence not having same number in adding with different values we have 15 sets of values for one time.

This can be interchange the values

Like that the example x1+x2+x3+x4=21

0+6+7+8=21,then 8+7+6+0=21 or 0+6+8+7=21,0+7+6+8=21.....etc

This means Number of different solutions to the equation x1+x2+x3+x4=21,0=<xi=<9 is 4^15solutions