Question

let N be the number of 8 digit number the sun of whose digit is 4. find n/12​

Answer 1

Answer:

We need to find the number of 8-tuples (  ) of non-negative integers such that  and  = 4. If .

There are three possibilities : 

Either exactly three among  equal 1 and the rest equal zero, 

or 

Five of them are zero and the other two equal 1 and 2, 

or 

Six of them are zero and the other equals 3. 

In the rest case, there are(7/5 ) = 35 such 8-tuples, 

In the second case there are(7/2)  = 42 such 8-tuples 

and in the third case there are 7 such 8-tuples. 

If  then either six of a2 a3,...,..a7 are zero and the other equals two, or five of them are zero and the remaining two both equal 1. 

In the former case, there are 7 such 8-tuples and in the latter case there are  = 21 such 8-tuples. 

If  then exactly six of  are zero and the other equals one. 

 .•.7 such 8-tuples. 

Finally, there is one 8-tuple in which  . 

.•. there are 120 such 8-tuples.

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