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  4. A four digit number is to be formed using the digits 1 , 2 , 3 , 4 , 5 , 6 , 7 (no digit is being repeated in any number). Then, the probability that it is > 4000 , is

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Q. A four digit number is to be formed using the digits $ 1 $ , $ 2 $ , $ 3 $ , $ 4 $ , $ 5 $ , $ 6 $ , $ 7 $ (no digit is being repeated in any number). Then, the probability that it is $ > 4000 $ , is

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Solution:

Total cases $={ }^{7} P_{4}=840$
Favourable cases $=4 \times 6 \times 5 \times 4=480$
$\therefore $ Required probability $=\frac{480}{840}=\frac{4}{7}$