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Question

Find the number of numbers, greater than a million, that can be formed with the digits 2,3,0,3,4,2,3.

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Solution

Total number of digits = 7

Since, 0 cannot be first digit of the 7 digit numbers.

Number of 6 -digit

Number =6!2!3!

[ 2 comes 2 times and 3 comes 3 times]

= 6×5×4×3!2×3!

= 6×5×2

= 60.
Now, number of 7-digit numbers = 7!2!3!

= 7×6×5×4×3!2×3!

= 7×6×5×2

= 420
Hence, total number of numbers which is greater then 1 million = 420-60= 360.


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