NCERT Class XI Mathematics - Permutations and Combinations - Solutions

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Question : 12
Total: 41
How many 4-digit numbers are there with no digit repeated?
Solution:  
The 4-digit numbers are formed from digits 0 to 9. In four digit numbers 0 is not taken at thousand’s place, so thousand’s place can be filled in 9 different ways. After filling thousand’s place, 9 digits are left. The remaining three places can be filled in
9
‌
P3
ways.
So the required 4-digit numbers = 9 ×
9
‌
P3
= 9 × 504 = 4536
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