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JEE MATHEMATICS MCQ: COMBINATIONS

1 Easy

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Application +4 | -1

The value of the expression

{ }^{47} C_4+\sum\limits_{{j=1}}^5 {}^{(52-j)} C_3

is equal to

View answer and explanation

Correct option: C

{ }^{52} C_4

Option C (

{ }^{52} C_4

) is correct because the expression simplifies to

{ }^{52} C_4

using the identity

{ }^{n+1} C_r={ }^n C_r+{ }^n C_{r-1}

repeatedly.

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{\;^{n + 2}}{C_8}:{\;^{n - 2}}{P_4} = \frac{{57}}{{16}}

n