how many 3 digits are there such that the digit at hundred's place is less than the digit in middle & the digit at unit's place is less than the digit in middle?. Repetition not allowed.

• Ans would be 204
  because
  if we take _9_ as middle number then we have 8 nos. for hundred's place(1,2,3,4,5,6,7,8) similarly for unit digit we have 8 nos.( since 0 is also included)
  so we have 8*1*8=64
  Similarly,
  7*1*7=49
  6*1*6=36
  5*1*5=25
  4*1*4=16
  3*1*3=9
  2*1*2=4
  1*1*1=1
  On adding 64+49+36+25+16+9+4+1=204
  
• 9 years agoHelpfull: Yes(51) No(13)
• middle no. should be between 2 to 9 to make it greater than unit's and hundred's place
  such as->120, 132, 231
  if middle place is 2 there is 1 possibility
  if middle place is 3 there are 2P2 possibilities--- 2 ( +2 to inc 0 in hundredth place) ----4
  if middle place is 4 there are 3P2 possibilities----6 ( +3 to inc 0 in hundredth place)---9
  similarly, for 5 --- 4P2 possibilities-----12 ( +4 to inc 0 in hundredth place) ----16
  6---5P2---20 ( +5 to inc 0 in hundredth place) -----25
  7---6P2---30 ( +6 to inc 0 in hundredth place) -----36
  8---7P2---42 ( +7 to inc 0 in hundredth place) -----49
  9---8P2---56 ( +8 to inc 0 in hundredth place) -----64
  
  hence, 1+4+9+16+25+36+49+64 = 204 .
• 9 years agoHelpfull: Yes(13) No(1)
• the right ans is 203
• 8 years agoHelpfull: Yes(1) No(0)
• ans:343
  1st position filled by 7 ways=7(1-7,bcz 2nd & 3rd position should greater )
  2nd position filled by 7 ways=7
  3rd also by 7 ways 7
  so,7*7*7=343
• 8 years agoHelpfull: Yes(0) No(4)
• 140 would be the ans.
  because middle no will be always greater than hundred and unit digit
  
• 8 years agoHelpfull: Yes(0) No(2)
• 249
  since 100th place =8 ways {12 ..8}
  10th place = 1 ways 9
  1st place = 9 ways {0, 1 , 2,3.....8}
  so when 10 th place 9 then 81
  8 then 56
  7 then 42
  6 then 30
  ..
  2 then 2 so total = 249
• 8 years agoHelpfull: Yes(0) No(2)
• the answer will be 92
• 8 years agoHelpfull: Yes(0) No(2)
• ans= 240
  @NEHA if we take _9_ at midle place then we have 8 options (1 2 3 4 5 6 7 8) for 100s place and 9 options (0 1 2 3 4 5 6 7 8 ) for 10s place what makes total 72 nos for 9 at middle space.
  like that for 8 at middle space we have total (7*8)= 56 nos
  for 7 at middle space we have total (6*7) = 42 nos
  ........................repeat like that up to _2_ at middle space(because if you take 1 at middle space there would be no combinations)
• 8 years agoHelpfull: Yes(0) No(1)
• correct ans is 542.
• 5 years agoHelpfull: Yes(0) No(0)