Latest Elitmus Aptitude Question SOLUTION: 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 al

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(#M40151819) ELITMUS Numerical Ability question permutation and combination Keep an EYE

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.

Asked In Elitmus KAR (9 years ago)

Unsolved Read Solution (9)

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Read Solution (9) :

Neha Gupta  (9 years ago)

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

Is this solution Helpfull? Yes (51) | No (13)  

akash verma  (9 years ago)

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 .

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vishal  (8 years ago)

the right ans is 203

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aswani bonga  (8 years ago)

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

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Soumen Maity  (8 years ago)

140 would be the ans.
because middle no will be always greater than hundred and unit digit

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vishal  (8 years ago)

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

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SHANUR RAHMAN  (8 years ago)

the answer will be 92

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Chandan Saurav Pradhan  (8 years ago)

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)

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Subhasikta Behera  (5 years ago)

correct ans is 542.

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