How many five digit numbers of different digits can be made in which digits are in 1.ascending order 2.descending order

Hi Ankush,

When digits need to be in ascending order, 0 can never be chosen.

So from the 9 digits (1,2,3,.....9) we select any five digits (which can be done in ⁹C₅ ways) and we can arrange the 5 selected digits in ascending order in only one way. So the number of 5 digit numbers in asceding order would be ⁹C₅.

When digits are in descending order (We can have 0 in the units place).

So from all the 10 digits, we select 5 digits in ¹⁰C₅ ways and we can arrange them in descending order in only one way.

So the number of 5 digit numbers in descending order will be ¹⁰C₅.

Hope that helps.

All the best.

Regards,

Ashwin (IIT Madras).