Question

how many sequences \[a_1,a_2,....a_k\] of non-negetive integers satisfy \[a_1+a_2+a_3....+a_k=n\]

Answer 1

Where are you stuck?

Answer 2

i am trying to make partition for all the sequence ,seperating with bars and stars

Answer 3

Bars an stars does give the aswer

Answer 4

**|**||****|*
trying k-1 bars for n stars

Answer 5

Yes

Answer 6

so
\[\left(\begin{matrix}n+k-1 \\ n\end{matrix}\right)\]

Answer 7

yes

Answer 8

@ganeshie
nice :)
so if we have : 1, 2, 3, 4
and, n = 20

then,
number of sequences is : (20+4-1) C 20
is it ?