Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:
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