Find the number of  5 letter words  that can be formed using the letters  of the word 'CONSIDER'

How many of them begin with 'C'

How many of them end with 'R' and 

How many of them begin with 'C' and end with 'R'

 

Number of 5 letter words that can be formed using the letters of the word CONSIDER is 
${}^{8}P_5=8\times 7\times 6\times 5\times 4=6720$
5 letters word begin with C
 

four places can be filled using O,N,S,I,D,E,R in ${}^{7}P_5$$=7\times 6\times 5\times 4=840$
 

5 letters word end with R

consider 5 places and fill the fifth place with can be R
first 4 places can be filled using C,O,N,S,I,D,E in ${}^{7}P_5$ ways
  ${}^{7}P_5$ $=7\times 6\times 5\times 4=840$
 

5 letters word begin with C and end with R
 

Consider 5 places fill C in first place . R in last place 
middle 3 places can be filled using O,N,S,I,D,E in ${}^{6}P_3$ ways
${}^{6}P_3=6\times 5\times 4=120$