MAH-CET 2025 — Mathematics PYQ

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Question

MAH-CET 2025 — Mathematics PYQ

MAH-CET | Mathematics | 2025

How many ways can a lawn tennis mixed double be made up from 7 married couples if no husband and wife play in the same time?

Choose the correct answer:

Explanation

1. Men ka selection (7 mein se 2):

\binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21

2. Women ka selection (7 - 2 = 5 bachi hui mahilaon mein se 2):

\binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10

3. Players ko teams mein arrange karne ke tareeke:

Ek mixed double match mein $M_1, M_2$ aur $W_3, W_4$ ke beech pairings aur side selection ke liye:

$M_1$ ke liye 2 positions (Team A ya Team B) = $2$
$M_2$ ke liye bachi hui 1 position = $1$
$W_3$ ke liye 2 possible partners ( $M_1$ ya $M_2$ ) = $2$
$W_4$ ke liye bacha hua partner = $1$

Total permutations per selection $= 2 \times 1 \times 2 \times 1 = 4$

4. Total Calculation:

\text{Total ways} = 21 \times 10 \times 4

\text{Total ways} = 840

Final Answer:

840