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There are 4 oranges, 5 apples and 6 mangoes in a basket. In how many ways can a person make a selection of fruits among the fruits in the basket?

A.

210

B.

209

C.

256

D.

220

Answer with explanation

Answer: Option BExplanation

Number of ways in which one or more objects can be selected out of S_{1} alike objects of one kind, S_{2} alike objects of second kind , S_{3} alike objects of third kind and so on … S_{n}alike objects of n^{th} kind

= (S_{1} + 1) (S_{2} + 1)(S_{3} + 1)…(S_{n} + 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

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