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Greatest Binomial Coefficients

The value of ...

Question

The value of $^{47} C_{4} + 5 \sum r = 1^{52 - r} C_{3}$ is equal to

A

^{47} C_{6}

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B

^{52} C_{5}

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C

^{52} C_{4}

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D

none of these

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Solution

The correct option is C $^{52} C_{4}$
We need value of $= {^{47} C}_{4} + \sum_{r = 1}^{5} {^{52 - r} C}_{3}$
$= {^{47} C}_{4} + {^{51} C}_{3} + {^{50} C}_{3} + {^{49} C}_{3} + {^{48} C}_{3} + {^{47} C}_{3}$
$= {^{51} C}_{3} + {^{50} C}_{3} + {^{49} C}_{3} + {^{48} C}_{3} + {^{47} C}_{3} + {^{47} C}_{4} = {^{51} C}_{3} + {^{50} C}_{3} + {^{49} C}_{3} + {^{48} C}_{3} + {^{48} C}_{4}$
$= {^{51} C}_{3} + {^{50} C}_{3} + {^{49} C}_{3} + {^{49} C}_{4} = {^{51} C}_{3} + {^{50} C}_{3} + {^{50} C}_{4}$
$= {^{51} C}_{3} + {^{51} C}_{4} = {^{52} C}_{4}$

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Similar questions

^{47} C_{4} + \sum_{j = 1}^{5}^{52 - j} C_{3} =

Q. The value of the expression

^{47} C_{4} + \sum_{j = 1}^{5}^{52 - j} C_{3}

Q. Find the value of

^{47} C_{4} + 5 \sum r = 1

^{52 - r} C_{3} = ?

Q. The value of

^{47} C_{4} + 5 \sum r = 1^{52 - r} C_{3}

=

$^{47} C_{4} + 5 \sum r = 1^{52 - r} C_{3}$ =

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