Number of ways in which one or more objects can be selected out of S1 alike objects of one kind, S2 alike objects of second kind , S3 alike objects of third kind and so on … Snalike objects of nth kind
= (S1 + 1) (S2 + 1)(S3 + 1)…(Sn + 1) – 1
Whenever it is not explicitly mentioned that fruits are distinct, we take them as identical. (Persons/men/women are normally considered as distinct.)
Hence, here we consider that
all 4 oranges are identical,
all 5 apples are identical
all 6 mangoes are identical.
As per the formula, required number of ways=(4+1)(5+1)(6+1)–1=5×6×7–1=209