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JEE 2023 Mathematics PYQ — Suppose Anil's mother wants to give 5 whole fruits to Anil from a… | Mathem Solvex | Mathem Solvex

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

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 oranges, 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:

Choose the correct answer:

A.
6860
(Correct Answer)
B.
6859
C.
6858
D.
6857

Correct Answer:

6860

Explanation

Calculation

\text{Total number of ways} = ^8C_2 \cdot ^7C_1 \cdot ^5C_2 + ^8C_2 \cdot ^7C_2 \cdot ^5C_1 + ^8C_3 \cdot ^7C_1 \cdot ^5C_1

= \left( \frac{8 \times 7}{2} \times 7 \times \frac{5 \times 4}{2} \right) + \left( \frac{8 \times 7}{2} \times \frac{7 \times 6}{2} \times 5 \right) + \left( \frac{8 \times 7 \times 6}{3 \times 2} \times 7 \times 5 \right)

= 1960 + 2940 + 1960 = 6860

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Explanation

Calculation

$\text{Total number of ways} = ^8C_2 \cdot ^7C_1 \cdot ^5C_2 + ^8C_2 \cdot ^7C_2 \cdot ^5C_1 + ^8C_3 \cdot ^7C_1 \cdot ^5C_1$

$= \left( \frac{8 \times 7}{2} \times 7 \times \frac{5 \times 4}{2} \right) + \left( \frac{8 \times 7}{2} \times \frac{7 \times 6}{2} \times 5 \right) + \left( \frac{8 \times 7 \times 6}{3 \times 2} \times 7 \times 5 \right)$

$= 1960 + 2940 + 1960 = 6860$

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