JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Permutations and Combinations

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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 ______.

Answer: 6860

Solution

Needing at least two oranges, at least one red apple and at least one white apple among five fruits forces the orange count to be two or three. The admissible splits (orange, red, white) are

(2, 1, 2)

(2, 2, 1)

and

(3, 1, 1)

. From

8

oranges,

7

red and

5

white apples these count as

(2 8) (1 7) (2 5) = 1960

(2 8) (2 7) (1 5) = 2940

and

(3 8) (1 7) (1 5) = 1960

. Their sum is

6860

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Integer answer

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