Question

Find x, if 10C5 + 10C6 + 11C, = 12C%.​

Answer 1

Answer:

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$.0 { { {5 {5465}^{?} }^{?} }^{?} }^{?}$

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Step-by-step explanation:

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Answer 2

SOLUTION

TO DETERMINE

The value of x when

$\sf{ {}^{10}C_5 + {}^{10}C_6 + {}^{11}C_7 = {}^{12}C_x }$

FORMULA TO BE IMPLEMENTED

$\sf{ {}^{n}C_r + {}^{n}C_{r + 1} = {}^{n + 1}C_{r + 1} }$

EVALUATION

$\sf{ {}^{10}C_5 + {}^{10}C_6 + {}^{11}C_7 = {}^{12}C_x }$

$\sf{ \implies \:{}^{11}C_6 + {}^{11}C_7 = {}^{12}C_x \: \: (\because \: \sf{ {}^{n}C_r + {}^{n}C_{r + 1} = {}^{n + 1}C_{r + 1} })}$

$\sf{ \implies \:{}^{12}C_7 = {}^{12}C_x \: \: (\because \: \sf{ {}^{n}C_r + {}^{n}C_{r + 1} = {}^{n + 1}C_{r + 1} })}$

$\sf{ \implies \:{}^{12}C_x = {}^{12}C_7 \: \: }$

Comparing both sides we get x = 7

FINAL ANSWER

Hence the required value of x = 7

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