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Q.

How many numbers greater than 10 lakhs will be formed from 2, 3, 0, 3, 4, 2, 3?

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a

420

b

360

c

400

d

300

answer is B.

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Detailed Solution

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All seven digits are included in any number that is greater than one million.
The number of arrangements of seven digits =7!2!×3!
=7×6×5×4×3!2!×3!
=7×6×5× 2
=420
Now, there are 6 digits, with 0 set at the millionth position, 2, 3, and 3 twice, and the other digits being different.
These 6 digits can be arranged = 6!2!×3!
=6×5×4×3!2!×3!
=6×5×2
=60 ways
Hence, the number of required numbers =420-60=360 

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How many numbers greater than 10 lakhs will be formed from 2, 3, 0, 3, 4, 2, 3?