Mathematics 2011 JAMB Past Questions - Question 47: In how many ways can the letter of the word FLATION be arranged ?

Correct Answer

B

Explanation

ELATIONsince there are 7 letters. the first letter can be arranged in 7 ways, the second letter in 6 ways, the third letter in 5 ways, the 4th letter in four ways, the 3rd letter in 3 ways and the 2nd letter in 2 ways and the last in one way.therefore 7 x 6 x 5 x 4 x 3 x 2 x 1 = 7! ways.The word "FLATION" has 7 letters. To find the number of ways the letters can be arranged, we can use the concept of permutations.Since all the letters in "FLATION" are unique, we can use the formula for permutations of distinct objects:n! / (n - r)!Where n is the total number of objects (letters) and r is the number of objects (letters) to be arranged.In this case, n = 7 (number of letters in "FLATION").Therefore, the number of ways the letters of the word "FLATION" can be arranged is:7! / (7 - 7)!= 7! / 0!= 7! / 1= 7!Calculating 7! (7 factorial):7! = 7 * 6 * 5 * 4 * 3 * 2 * 1= 5040Therefore, there are 5040 ways the letters of the word "FLATION" can be arranged.