Question

find r if 16C4 +16C5 +17C6 + 18C7 =19Cr​

Answer 1

SOLUTION

GIVEN

$\sf{ {}^{16} C_4 + {}^{16} C_5+ {}^{17} C_6+ {}^{18} C_7 = {}^{19} C_r }$

TO DETERMINE

The value of r

FORMULA TO BE IMPLEMENTED

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

EVALUATION

$\sf{ {}^{16} C_4 + {}^{16} C_5+ {}^{17} C_6+ {}^{18} C_7 = {}^{19} C_r }$

$\sf{ \implies {}^{17} C_6+ {}^{17} C_6+ {}^{18} C_7 = {}^{19} C_r }$

$\sf{ \implies {}^{18} C_6+ {}^{18} C_7 = {}^{19} C_r }$

$\sf{ \implies {}^{19} C_7 = {}^{19} C_r }$

$\sf{ \implies r = 7}$

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