JAMB Mathematics 2019 Paper

Concept:Arrangements of a word with repeated letters use the permutation formula for indistinguishable objects.Explanation:The word MATHEMATICIAN contains 13 letters in total.Count the repeated letters: M appears 2 times, A appears 3 times, T appears 2 times, and I appears 2 times.All other letters, H, E, C, N, each appear only once.The number of distinct arrangements is:$$\frac{13!}{2! \times 3! \times 2! \times 2!}$$First, $13! = 6227020800$.The denominator is $2! \times 3! \times 2! \times 2! = 2 \times 6 \times 2 \times 2 = 48$.So, the arrangement count is:$$\frac{6227020800}{48} = 129729600$$Therefore, MATHEMATICIAN can be arranged in 129729600 distinct ways.Answer:$129729600$ ways, which is Option D.