Concept:This problem uses permutations of letters with repetition.
When identical letters appear, divide the total factorial by the factorial of the repeated count.
Explanation:The word ZOOLOGY contains 7 letters: Z, O, O, L, O, G, Y.
The letter O occurs 3 times; all other letters occur once.
Total arrangements if all letters were distinct would be
7!.
Since the three O's are identical, divide by
3! to avoid counting repeated swaps of the O's.
So the number of arrangements is:
3!7!=3!7×6×5×4×3!=7×6×5×4=840.Thus, there are 840 distinct arrangements of ZOOLOGY.
Answer:840 ways (Option C).