JAMB Mathematics 2017 Paper

Concept:Arrangements of letters with repeated items use factorial division.Explanation:The word EXCELLENCE has 10 letters in total.The repeated letters are E (4 times), C (2 times), and L (2 times).When arranging $10$ letters, start with $10!$.Divide by the factorial of each repeated letter count to remove identical arrangements.So the number of ways is:$$\frac{10!}{4! \times 2! \times 2!}$$This matches option C.Answer:$$\frac{10!}{4!2!2!}$$Option C.