Counting principle and permutations – UGC NET Question

Statements A, B and D are correct. A states the multiplication principle for independent choices. B defines permutations as ordered arrangements. D is true because there are n! ways to arrange n distinct objects. C is false; the formula for permutations of n distinct objects taken r at a time is nPr, and E is false because identical objects reduce the number of distinct permutations below n!. Thus A, B and D only are correct.

Option A:
Option A is correct as it includes the standard counting principle, the definition of permutations and the basic n! formula, while excluding C and E, which misapply combinatorial formulas.

Option B:
Option B is incorrect since it adds C, incorrectly using nCr in place of nPr for permutations, and so combines an error with correct statements.

Option C:
Option C is wrong because it also includes E, claiming n! permutations even with identical objects, and therefore contains two incorrect statements.

Option D:
Option D is incomplete as it drops A and leaves only B, D and E, losing the foundational multiplication principle and adding E, which contradicts the effect of identical objects.