I need to find the number of solutions to $$a+b+c+d+e+f=14$$ where $a,b,c,d,e$ and $f$ are whole numbers $\le 4$.
Manually I am getting the result which is $1506$, but is there any other method that solves the problem easily?
EDIT: Actually this is the question of cricket I converted it into the following problem:
In Indo-Pak one day International cricket match at Sharjah, India needs $14$ runs to win just before the start of the final over. Find the number of ways in which India just manages to win the match (i.e. scores exactly $14$ runs), assuming that all the runs are made off the bat & the batsman can not score more than $4$ runs off any ball.