112 oranges, 56 apples and 140 pears are equally packed in cartons so that no fruit is left. Ankit
says, 56 is the highest number of fruits he can equally pack in each box. Evaluate if Ankit is correct or
not. Show your working
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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
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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