If `\ ^n C_4=\ \ ^n C_6`, find`. ^(12)C_ndot`

Explanation

We have,


`\ ^{n} C_{4}=\ ^{n} C_{6} `


`Rightarrow n=6+4=10[because\ ^{n} C_{x}=\ ^{n} C_{y} Rightarrow x=y] or, n=x+y `


Now, `\ ^{12} C_{10}=\ ^{12} C_{2}[because\ ^{n} C_{r}=\ ^{n} C_{n-r}] `


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