Find the number of permutations of the letters of the word ‘ENGLISH’. How many of these begin with E and end with I?
There are 7 letters in the word ENGLISH.
Permutation of 7 letters in 7 places can be done in P(7,7) ways.
Formula:
Number of permutations of n distinct objects among r different places, where repetition is not allowed, is
P(n,r) = n!/(n-r)!
Therefore, a permutation of 7 different objects in 7 places is
P(7,7) = 
= 
= 
= 5040.
Hence, the total number of permutations is P 5040.
To find a number of words starting with E and ending with I, let us consider their position which is 1st and 7th.
The rest 5 letters are to be arranged in 5 places which can be done in P (5,5)
Formula:
Number of permutations of n distinct objects among r different places, where repetition is not allowed, is
P(n,r) = n!/(n-r)!
Therefore, a permutation of 5 different objects in 5 places is
P(5,5) = 
= 
= 
= 120.
Therefore, there are 120 words starting with E and ending with I.