Question

Hey guys ....

⭐⭐ Kindly help me with this sum as soon as possible ⭐⭐

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Refer the following pic .

please help me guys

Answer 1

hope u like my process
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formula to be used
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$\large{ \boxed{ \bf= > {}^{n} C _{r + 1} + {}^{n} C _{r} = {}^{n + 1} C_{r + 1} }}$

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$= > \bf {}^{47} C _{4} + \displaystyle \bf \sum_{j = 1}^{5} {}^{52 - j} C _{3} \\ \\ \it = {}^{47} C _{4} + {}^{51} C _{3} + {}^{50} C _{3} + {}^{49} C _{3} + {}^{48} C _{3} + {}^{47} C _{3} \\ \\ = \it ({}^{47} C _{4} + {}^{47} C _{3}) + {}^{48} C _{3} + {}^{49} C _{3} + {}^{50} C _{3} + {}^{51} C _{3} \\ \\ = \it \: ({}^{48} C _{4} + {}^{48} C _{3}) + {}^{49} C _{3} + {}^{50} C _{3} + {}^{51} C _{3} \\ \\ = \it ( {}^{49} C _{4} + {}^{49} C _{3}) + {}^{50} C _{3} + {}^{51} C _{3} \\ \\ = \it( {}^{50} C _{4} + {}^{50} C _{3}) + {}^{51} C _{3} \\ \\ = \it {}^{51} C _{4} + {}^{51} C _{3} \\ \\ = \underline{ \bf \: {}^{52} C _{4}}$

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