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Question
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
Options
420
360
400
300
Solution
360
10 lakhs consists of seven digits.
Number of arrangements of seven numbers of which 2 are similar of first kind, 3 are similar of second kind =\[\frac{7!}{2!3!}\]
But, these numbers also include the numbers in which the first digit has been considered as 0. This will result in a number less than 10 lakhs. Thus, we need to subtract all those numbers.
Numbers in which the first digit is fixed as 0 = Number of arrangements of the remaining 6 digits =\[\frac{6!}{2!3!}\]
Total numbers greater than 10 lakhs that can be formed using the given digits =\[\frac{7!}{2!3!}\] -\[\frac{6!}{2!3!}\]
420-60
= 360
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