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

Correct option is A.220Find the total number of waysGiven that there are 31 Objects in which 10 are identical and 21 are distinctThe number of ways of choosing 0 identical and 10 distinct=1× 21CThe number of ways of choosing 1 identical and 9 distinct=1× 21CThe number of ways of choosing 2 identical and 8 distinct=1× 21CThe number of ways of choosing 3 identical and 7 distinct=1× 21CThe number of ways of choosing 4 identical and 6 distinct=1× 21CThe number of ways of choosing 5 identical and 5 distinct=1× 21CThe number of ways of choosing 6 identical and 4 distinct=1× 21CThe number of ways of choosing 7 identical and 3 distinct=1× 21CThe number of ways of choosing 8 identical and 2 distinct=1× 21CThe number of ways of choosing 9 identical and 1 distinct=1× 21CThe number of ways of choosing 10 identical and 0 distinct=1× 21C[ nC0+ nC1+ nC2+. nCn=21C0+ 21C1+ 21C2 2121C11+ 21C12. 21[nCr=nCn−rTotal number of ways= 21C0+ 21C1+ 21C2... 21C10=2212Hence option (A) is correct