Alphabetical Angle
If all the arrangements of the letters in the word ANGLE are written down in alphabetical order, what position does the word ANGLE occupy?
Age
14 to 16
Challenge level
Problem
There are 120 different arrangements of the five letters in the word ANGLE. If all 120 are listed in alphabetical order starting with AEGLN and finishing with NLGEA, which position in the list does ANGLE occupy?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
There are 24 arrangements of the letters in the word ANGLE with A as the first letter (the number of ways of arranging the other 4 letters is $4\times3\times2\times1$). In alphabetical order AEGLN is first and ANLGE is last. ANLEG is the 23rd and hence ANGLE is in the 22nd position on the list.