The Number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is:

Step-by-step solution

There is only one way in which we can choose one, two or more objects from 10 identical objects. Number of ways of selecting 10 objects =   21 C 10 +   21 C 9 +   21 C 8 +   21 C 7 +   21 C 6 +   21 C 5 +   21 C 4 +   21 C 3 +   21 C 2 +   21 C 1 +   21 C 0 We know   n C r =   n C n - r and ⇒ 2 21 =   21 C 0 +   21 C 1 +   21 C 2 +   21 C 3 +   21 C 4 + . . . . . . . . . +   21 C 21   &