Question:

If $^{30}C_{r+2} = {^{30}C_{r-2}}$, then r equals :

Updated On: Jul 6, 2022

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The Correct Option is B

Solution and Explanation

Let $^{30}C_{r+2} = {^{30}C_{r-2}}$ ......(1) We know, If $^nC_{r_1} = {^{n}C_{r_2}}$ then $r_1 + r_2 = n $ In above given equation (1) we have $n = 30, r_1 = r + 2, r - 2 = r_2$ $\therefore \, r_1 + r_2 = r + 2 + r - 2 = 2r$ and $n = 30$ $\therefore \, 2r = 30 \, \Rightarrow \, r = 15$

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Concepts Used:

Permutations and Combinations

Permutation:

Permutation is the method or the act of arranging members of a set into an order or a sequence.

In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
A permutation is used in many events of daily life. It is used for a list of data where the data order matters.

Combination:

Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.

Combination refers to the combination of about n things taken k at a time without any repetition.
The combination is used for a group of data where the order of data does not matter.