How many three-digit numbers can be generated from 1, 2, 3, 4, 5, 6, 7, 8, 9 such that the digits are in ascending order

examrobotsa's picture
Q: 68 (IAS/2009)
How many three-digit numbers can be generated from 1, 2, 3, 4, 5, 6, 7, 8, 9 such that the digits are in ascending order

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,5,0,3,2,3

keywords: 

{'digit numbers': [0, 0, 1, 0], 'digits': [0, 0, 3, 2], 'order': [6, 12, 34, 35]}

The question is asking about the count of three-digit numbers that can be formed with the digits, 1, 2, 3, 4, 5, 6, 7, 8 and 9 in ascending order only.

Option 1 suggests there are 80 such numbers. This is not accounting for all the combinations possible.

Option 2 recommends 81 such numbers. Again, all combinations have not been considered in this count.

Option 3 insists there are 83 such numbers. Once more, the counting is not accurate as it is less than the actual count.

Option 4 states there are 84 such numbers. This is indeed the correct count. With 9 digits, we want to find the number of ways to choose 3 to put in ascending order. The number of ways to pick 3 numbers out of 9 (order doesn`t matter) is given by the binomial coefficient "9 choose 3", which is calculated as 9! / (3!(9-3)!) = 84.

So, the correctly dissected answer is option 4 - 84.