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

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

Grade:12

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

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).

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