Latest Elitmus Aptitude Question SOLUTION: abc is 3-digit number in which atleast 2 digits are equal. How many number can formed from this combination option a) 225 b) 234 c) 243 d) 250

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(#M40024315) ELITMUS question elitmus Keep an EYE

abc is 3-digit number in which atleast 2 digits are equal. How many number can formed from this combination
option
a) 225
b) 234
c) 243
d) 250

Asked In Elitmus rohit kumar (11 years ago)

Unsolved Read Solution (9)

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Read Solution (9) :

Ajit Kumar  (11 years ago)

3 digits no. having none of the digits equal= 9*9*8=648
total no. of 3 digits no.= 900
so, 3 digit no. in which atleast 2 digits are equal= 900-648= 252
i think u lost the options that were in the xam

Is this solution Helpfull? Yes (24) | No (2)  

rohit kumar  (11 years ago)

i think 243 will be correct i.e. _ _ _ fix two 1 at lest most corner then unit digit can be filled in 0,2,3,4,5,6,7,8,9.suppose if we take 2 at unit place this can arranged in 3!/2! similarly other digit like that total 8*3=24 now 11 place can be in nine different way 11,22,33,44 .... upto 99 so total number without zero is 24*9=216+9(111 or222 or333 up to 999)+if zero is included then 2*=18
i.e total 216+18+9=243

Is this solution Helpfull? Yes (12) | No (5)  

anshu  (11 years ago)

990-648
=252

Is this solution Helpfull? Yes (11) | No (6)  

Ankit Goyal  (11 years ago)

There are 3 cases

X?X (1st and 3rd digit equal) = 9 * 10 = 90 cases (X can be any digit from 1 to 9 and ? can be any digit (0-9))
XX? = 90 cases (X (1-9) ?(0-9))
?XX = 90 cases

but the case in which all the three digits are same i.e. 222,333,444,555...
is repeated in all the above three cases
so it should be considered only once
total cases = 270 - 20 = 250

Is this solution Helpfull? Yes (2) | No (1)  

vaibhav kumar   (11 years ago)

actually the option are.....
a)225
b)234
c)243
d)252
and the correct one is 252....and explanation is given by many one

Is this solution Helpfull? Yes (1) | No   

banashri borah  (11 years ago)

last option is 152 and it is the correct answer

Is this solution Helpfull? Yes | No (3)  

shashank sharma  (11 years ago)

100---999 3digit no..
who have 2 digit commn are--
100,101,110to119,121,122,131,133,finally knw the pattern--
accrding to option d)250(but actual 251 or 252)

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CRASH  (11 years ago)

Solution

10C1*9C1*3C1(numbers with 2 common digits) - 10C1*3C1(numbers which has selceted 0 as non repetitive number and placed it on hundreth place) - 10C1*3C2(numbers which has selected 0 as repetitive number and placed non zero digit at either unit or tenth place )

270 - 10 - 10 = 250

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animesh jian  (11 years ago)

total no form= 9*9*9= 729 {same no is also consider}
9*8*7= 504 {all are different }
729- 504= 225

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