UGC NET Questions (Paper – 1)

This option is correct because permutations count ordered arrangements of r objects chosen from n distinct objects. The standard notation for this is nPr. It takes into account both the selection and the ordering of the objects. Therefore, the correct symbol is nPr.

Option A:
nCr represents combinations, which count selections without regard to order. It does not distinguish between different arrangements of the same r objects. Since the question explicitly mentions arranging, this symbol is not appropriate.

Option B:
rPn is not the standard way of denoting arrangements of r out of n. It reverses the positions of n and r and does not correspond to any common formula in basic combinatorics. Hence, this notation is incorrect.

Option C:
The symbol nPr captures both how many objects are chosen and how they are ordered. It equals n!/(n−r)!, which counts all possible ordered selections. This matches the description of selecting and arranging r objects from n, so this option is correct.

Option D:
rCn would again reverse the roles of n and r in combination notation. It is not used to represent either permutations or combinations in standard texts. Therefore, it is not the correct symbol.