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  4. The value of expressions 47C4 + ∑5i = 1 ((52 - i)C3 =

Q. The value of expressions $^{47}C_4 + \sum^5_{i = 1} {^((52 - i)}C_3}$ =

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Solution:

$^{47}C_{4} + ^{51}C_{3} + ^{50}C_{3} + ^{49}C_{3} + ^{48}C_{3} + ^{47}C_{3} = ^{52}C_{4} $
by applying $^{n}C_{r} + ^{n}C_{r+1} = ^{n+1}C_{r+1}$

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