Find the value of $^{10} C_{5} + 2. (^{10} C_{4}) +^{10} C_{3}$ .

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Solution

$^{10} C_{5} + 2. (^{10} C_{4}) +^{10} C_{3} = \frac{10!}{5! .5!} + 2. \frac{10!}{6! .4!} + \frac{10!}{7! .3!} = 252 + 420 + 120 = 792$

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