JAMB Mathematics 2012 Paper

Concept:When a word has repeated letters, divide the total factorial by the factorial of each repeated letter count.Explanation:The word TOTALITY has 8 letters in total.The letter T appears 3 times.All other letters appear once, so they do not affect the division.Use the formula for arrangements with repetition:$$\frac{8!}{3!}$$Expand the factorials:$$\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3!}$$Cancel $3!$ from numerator and denominator:$$8 \times 7 \times 6 \times 5 \times 4 = 6720$$Answer:A. 6720