The number of 4 digit numbers with the first digit as 1 and having exactly two identical digits are

1) 256
2) 720
3) 486
4) 432

• ans. is "432"
  for four places we have 1 on first place.
  now we would divide work in two parts
  (1)When 1 is repeated: then we have to chose only 2 no. from remaining 9 no.s by 9C2 and their arrangement would be 3! so here we got 9C2*3! =216 ways.
  (2)when 1 is not repeated: then for it we again have to choose 2 no. from remaining 9 no.s by 9C2... Out of these 2 ,one no. would occur two times. and final arrangement is by (3!/2!) ways . thus here we get 9C2*(3!/2!)*2=216 ways.
  
  HENCE FINAL ANSWER = 216+216= 432
• 10 years agoHelpfull: Yes(2) No(0)