A fruit basket contains only Apples and Oranges. The ratio between the number of apples and oranges in the basket is 3 : 5. Ananya added 8 mangoes to the basket. The total number of fruits in the basket now became 24. What is the ratio between the numbers of Oranges and Mangoes in the basket?
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Whenever it is not explicity mentioned that fruit and distint, We take them as identical. 0 or more orange can be selected from 4 identical oranges in (4+1)=5 ways. 0 or more apples can be selected from 5 identical apples in (5+1)=6 ways.
0 or more mangoes can be selected from 6 identical mangoes in 7 ways.
∴ Total no. of ways in which all of three types of fruits can be selected (the no. of any type of fruits may also be 0),
5×6×7=210,
But in these 20 selection, there is one selection where all fruits are 0, hence we reduce 1 selection.
∴ the required no. =210−1=209
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