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2 votes
2 votes
How many 5 digit number are possible so that in each of these number every digit is greater than digit on its right?

2 Answers

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i solved like this

first lets take number from 1 to 9 then we can select any 5 numbers in 9C5 ways but we can arrange them only in one way.

now including 0 we can place it at only last position since at any other position it would not satisfy the condition.

so remaining place will be filled by all 9 digits that is 9C4

so total combination = 9C5 + 9C4 = 252.
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Once you pick 5 different digits, there is only one way to arrange them so that the digits are decreasing. I would view the answer as (9C5), but of course this is equal to (9C4).

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