How many permutations can be formed from all the letters in the word engineering?

Accepted Solution

Answer:277,200Step-by-step explanation:To find the number of permutation we can form from the letters of the word "engineering", we first need to find the frequencies of the different letters present.E = 3G = 2N= 3I = 2 R = 1Now that we have the frequencies, we count the number of letters in the word "engineering".E N G I N E E R I N G11 lettersNow we take the factorial of total number of letters and divide it by the number of repeats and their factorialSo we get:[tex]\dfrac{11!}{3!2!3!2!1!}[/tex]We remove the 1! because it will just yield 1.[tex]\dfrac{11!}{3!2!3!2!}[/tex]So the total number of permutations from the letters of the word "engineering" will be:Total number of permutations = [tex]\dfrac{39,916,800}{144}[/tex]Total number of permutations = 277,200