JAMB Mathematics 2017 Paper

Concept:Arranging letters with repeated items uses the formula for permutations of multiset: divide by the factorial of each repeated letter count.Explanation:The word MATHEMATICS has 11 letters in total.It contains repeated letters: M appears 2 times, A appears 2 times, and T appears 2 times.The total arrangements are $11!$ divided by the factorials of the repeated frequencies:$$\frac{11!}{2! \times 2! \times 2!}$$This accounts for the identical M's, A's, and T's that are indistinguishable during arrangement.Answer:$$\frac{11!}{2!2!2!}$$This matches option C.