Cool 6-Digit Numbers

Question

Let us call a -digit number cool if each of its digits is no less than the preceding digit. How many cool $6-$digit numbers are there?

Details And Assumptions:

• For example, $,112446  is cool.

• 233043 isn't cool.

Comments

Is it 14C5Lakshman Patel RJIT

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It is $\binom{14}{6}=3003$

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oh yes 14C6.

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please help with solution

Answer 1

first we should not that   0 can not be most significant bit

by this we canclude that 0 can not occur any where in cool no

and  this problem can be converted into  combination of 6 object from a set of 9 different object(1,2,3,4,5,6,7,8,9)

9+6-1C 9-1 =14C8=14C6

Comments

What about numbers like 155426?

Even they're coming in this way,

Plz Correct me if I'm wrong..

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@manoj  we have to find cool no and the defination of cool no is given in the question , that is  each of its digits is no less than the preceding digit which mean the digit of numbers should be in non decreasing order

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I'm having a doubt when we have

Numbers like 155468 here maybe when we are using n-1+r C r some wrong digits will creep in ?

If they are not coming plz help regarding that logic..

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in the answer, we are only selecting the digit and not arranging them