Question 8: In this exercise, we consider strings that can be obtained by reorde

Question

Question 8: In this exercise, we consider strings that can be obtained by reordering the letters of the word ENGINE. Determine the number of strings that can be obtained . Determine the number of strings in which the two letters E are next to each other . Determine the number of strings in which the two letters E are not next to each other and the two letters N are not next to each other. (You do not get marks if you write out all possible strings. You must use the counting rules that you learned in class.)

Explanation / Answer

1. No of strings formed by arranging letters of word "Engine" = 6!/(2!*2!)= 180

(Factorial of number of characters divided by factorial of number of repeated characters , in our case we have twice E and N so we divide 6! by 2! twice)

2. Lets assume EE are tied together as 1 character then toal number of distinct characters will be 5 therefore no of sting will be =5! = 120

3. Answer= Total Number of Strings-( Strings where E and N are next to each other, lets tie them as one character , then we will have total 3 characters in total)

=> Answer=180- 3!= 180-6=174

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