Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer 5 fruits to…

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Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer 5 fruits to Anil is _____ .

Aicharya · Accepted Answer

We have, $7$ Red apples $(RA)$ $5$ white apples $(WA)$ $8$ oranges $(O)$ Now, for offering $5$ fruits to be selected Possible selections :- $(2O, 1RA, 2WA)$ or $(2O, 2RA, 1WA)$, or $(3O, 1RA, 1WA)$ Required number of ways $= \binom{8}{2} \binom{7}{1} \binom{5}{2} + \binom{8}{2} \binom{7}{2} \binom{5}{1} + \binom{8}{3} \binom{7}{1} \binom{5}{1}$ $= 1960 + 2940 + 1960$ $= 6860$

Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and…

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