Strictly increasing!
Probability
Level
3
Find the number of 5 digit numbers which can be made with the digits from the set {0, 1, 2,..9} such that the digits are strictly increasing
The answer is 126.
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1 solution
Firstly, if you select 0, then it should be placed as the leading digit as it is always the smallest of the set. So you cannot choose 0.(I assumed that the leading digit cannot be 0)
So, choose any 5 distinct numbers from the rest of the set,i.e, from {1,2,3,4,5,6,7,8,9}. You can do this in ( 5 9 ) = 1 2 6 ways. Then arrange the numbers in ascending order to get exactly 1 number. Therefore, the total number of ways is 126