Mathematics 2012 JAMB Past Questions - Question 48: In how many ways can the letter of the word TOTALITY be arranged ?

Correct Answer

A

Explanation

81/31 = 8x7 .............x 3 x 2 x1= 8 x 7 x 6 x 5 x 4 = 6720To find the number of ways the letters of the word "TOTALITY" can be arranged, we can use the concept of permutations.The word "TOTALITY" has a total of 8 letters. However, it contains repeated letters: T appears twice, O appears twice, and the remaining letters (A, L, I, and Y) are all unique.To calculate the number of arrangements, we divide the total number of arrangements of all the letters by the number of arrangements of the repeated letters.The total number of arrangements of all the letters is given by 8!, which is the factorial of 8 (8 factorial).However, since the letter T appears twice and the letter O appears twice, we need to divide the total number of arrangements by 2! (the factorial of 2) for each of these repeated letters.Therefore, the number of ways the letters of the word "TOTALITY" can be arranged is:8! / (2! * 2!) = (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 2 * 1) = 40,320 / 4 = 10,080Therefore, there are 10,080 ways to arrange the letters of the word "TOTALITY".