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Q.
The number of solution to the equation $2a+3b+6c=60,$ where $a,b,c\in N$ , is equal to
NTA AbhyasNTA Abhyas 2020Permutations and Combinations
Solution:
$2a+3b+6c=60$
Note that $3b,6c,60$ are divisible by $3,$ hence $2a$ is divisible by $3$
Similarly $2a,6c,60$ are even numbers hence $3b$ is an even number
Therefore $a=3k_{1},b=2k_{2}$
So the equation reduces to $k_{1}+k_{2}+C=10,\forall k_{1},k_{2},C\in N$
Hence, the number of solutions $=\_{}^{9}C_{2} = 36$