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  4. If 10Cx = 10Cx + 4, find the value of x.

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Q. If ${^{10}C_{x}} = {^{10}C_{x + 4}}$, find the value of x.

Permutations and Combinations

Solution:

We have ${^{10}C_{x}} = {^{10}C_{x+4}}$
$\Rightarrow \, x + x + 4 = 10 \, \Rightarrow \, 2x = 6 \, \Rightarrow \, x = 3$