i) Find the no of 4 letter words that can be
formed using the letter of the word
EQUATION
(i)How many of them begin with the letter E
(ii)How many of them end with the letter N
(iii) How many of them begin with E and end with N

Given word EQUATION 

Number  of 4 letters words using given  word EQUATION =${}^{8}P_4=1680$
1.How many of them begin with E:
The first place can be filled with E.

The remaining 3 places can be filled with 7 letters = ${}^{7}P_3$   ways
= 210 

total no.of 4 letter words that begin with E = 210

2. How many of them end with N
The last place can be filled ‘N’

The remaining 3 places can be filled with remaining 7 letters in ${}^{7}P_3$ ways
= 7 × 6 × 5 = 210
The required no of 4 letter words end with N
= 210 × 1 = 210

3. How many words begin with E and end
with N

The first place can be filled with E and last place can be filled with N remaining 6 letters in ${}^{6}P_2$ ways
Required no of 4 letter words begin with E and
end with N = ${}^{6}P_2$
= 6 × 5 = 30