MAH-CET 2025 — Mathematics PYQ

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Question

MAH-CET 2025 — Mathematics PYQ

MAH-CET | Mathematics | 2025

How many five-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?

Choose the correct answer:

Explanation

Mathematical Calculation:

1. Total Digits:

$\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$ (Kul 10 digits)

2. Fixed Positions:

Telephone number 5-digit ka hai aur pehle do digits 6 aur 7 fixed hain:

[6] [7] [\_] [\_] [\_]

3. Remaining Digits:

Kyunki repetition allowed nahi hai, isliye 6 aur 7 ko hatane ke baad bache hue digits:

10 - 2 = 8 \text{ digits}

4. Remaining Positions:

Humein bachi hui 3 jagahon ko bharna hai:

Teesre digit ke liye choices: 8
Chauthe digit ke liye choices: 7
Paanchve digit ke liye choices: 6

5. Total Ways:

\text{Total Numbers} = 1 \times 1 \times 8 \times 7 \times 6

\text{Total Numbers} = 8 \times 7 \times 6

\text{Total Numbers} = 336