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Maths-

General

Easy

Question

$blank to the power of 47 C subscript 4 plus sum from j equals 1 to 5 of to the power of 52 minus j end exponent C subscript 3$ is equal to

${}^{52}C_{4}$
${}^{51}C_{4}$
${}^{52}C_{3}$
${}^{51}C_{3}$

hint Hint:

To solve the question first we have to expand the sigma where we will put the value of j from 1 to 5 each at a time then we will solve using $blank to the power of n C subscript r space end subscript plus to the power of n C subscript r minus 1 end subscript equals to the power of n plus 1 end exponent C subscript r space$ .

The correct answer is: $C presuperscript 52 subscript 4$

$blank to the power of 47 C subscript 4 plus sum from j equals 1 to 5 of to the power of 52 minus j end exponent C subscript 3$
$blank to the power of 47 C subscript 4 plus to the power of 52 minus 1 end exponent C subscript 3 plus to the power of 52 minus 2 end exponent C subscript 3 plus to the power of 52 minus 3 end exponent C subscript 3 plus to the power of 52 minus 4 end exponent C subscript 3 plus to the power of 52 minus 5 end exponent C subscript 3 equals to the power of 47 C subscript 4 plus to the power of 51 C subscript 3 plus to the power of 50 C subscript 3 plus to the power of 49 C subscript 3 plus to the power of 48 C subscript 3 plus to the power of 47 C subscript 3$
using $blank to the power of n C subscript r space end subscript plus to the power of n C subscript r minus 1 end subscript equals to the power of n plus 1 end exponent C subscript r space$
$equals to the power of 48 C subscript 4 plus to the power of 51 C subscript 3 plus to the power of 50 C subscript 3 plus to the power of 49 C subscript 3 plus to the power of 48 C subscript 3 equals to the power of 49 C subscript 4 plus to the power of 51 C subscript 3 plus to the power of 50 C subscript 3 plus to the power of 49 C subscript 3 equals to the power of 50 C subscript 4 plus to the power of 51 C subscript 3 plus to the power of 50 C subscript 3 equals to the power of 51 C subscript 4 plus to the power of 51 C subscript 3 equals to the power of 52 C subscript 4$

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