combination

Question

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

Comments

@srestha,what if here no repetition is allowed?

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But the digits are already not repeated Devshree Dubey

Or did you mean if repetition is allowed?

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@MiNiPanda,Yes if the repetition is allowed in that case?

Answer 1

The condition of every digit is grater than the next right digit makes a decreasing sequence of 5 digits. example 8,5,3,2,1 or 6,4,3,2,0.

We have total ten digits 0,1,2...9 and in decreasing order :

9,8,7,6,5,4,3,2,1,0

We can pick any five of them from the above sequence and form our required 5 digit number. We cant not permute the selected numbers.

So total no of required numbers = No of ways we can select 5 elements out of 10 from above sequence = $\binom{10}{5}$

Comments

One variation of above question: every digit is less than digit on its right hand side.

{1,2,3,4,5,6,7,8,9}

In this case answer will be 9C5=126