Official solution
For alike n objects, number of ways we can select zero or more objects = n + 1 and number of ways we can select at least one object = n
Given 10 identical white balls, 9 identical green balls and 7 identical black balls.
To find number of ways for selecting atleast one ball.
Number of ways to choose zero or more white balls = (10 + 1) [since, all white balls are mutually identical]
Number of ways to choose zero or more green balls = (9 + 1) [since, all green balls are mutually identical]
Number of ways to choose zero or more black balls = (7 + 1) [since, all black balls are mutually identical]
Hence, number of ways to choose zero or more balls of any colour = (10 + 1) (9 + 1) (7 + 1)
Also, number of ways to choose a total of zero balls = 1
Hence, the number, if ways to choose at least one ball (irrespective of any colour) = (10 + 1) (9 + 1) (7 + 1) - 1 = 879