Latest CTS Aptitude Question SOLUTION: how many number of 3 digit numbers can be formed usingzs numbers 1,2,3,4 in which 1 number can be repeated..?

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how many number of 3 digit numbers can be formed usingzs numbers 1,2,3,4 in which 1 number can be repeated..?

Asked In CTS Vinoth kumar (10 years ago)

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Read Solution (10) :

Ravi teja Manukonda  (10 years ago)

ambiguity in question
If 1 number can be repeated for any no of times then
4*4*4 = 64
If 1 number can be repeated for one time then
4*4*3 = 48

Is this solution Helpfull? Yes (28) | No (1)  

Shanu Dutta  (10 years ago)

sorry 48
4*4*3 = 48

Is this solution Helpfull? Yes (15) | No (3)  

Shanu Dutta  (10 years ago)

For first place any of the 4 number can be placed, for 2nd place again any of the 4 number can be placed as 1 number can be(not has to be)repeated, for 3rd place any of the remaining 3 numbers can be placed
4*4*3=36

Is this solution Helpfull? Yes (2) | No (11)  

shruti tiwaskar  (10 years ago)

64 is the answer

Is this solution Helpfull? Yes (2) | No (4)  

renati pallavi  (10 years ago)

take 3 postions _ _ _
1 can be repeated as 3,2,1,0
3 times repetition case: 1 1 1
2 times repetition case:one place can be selected and filled with any of numbers(2,3,4)=3c1*3
1 time repetition case:2 places can be selected and filled with any numbers(2,3,4)=3C2*3*2
ans:1+9+18

Is this solution Helpfull? Yes (1) | No   

siddagalla bhaskar  (10 years ago)

we can take this prblm as the 3 digit number without 1, 1 repeated for one time, 1 repeated for two times and 1 repeated for 3 times.

without repetition of 1:- 3! =6
1 repeated once:- 3*3P2 =18
1 repeated twice:- 2*3 =6
1 repeated thrice:- 1 =1

total numbers can be formed are: 31

Is this solution Helpfull? Yes (1) | No   

pragyanpradhan  (10 years ago)

if all place contain 1,than it is in 1 way i.e 1*1*1
if 2 place contain 1,it is in 9 ways=3*3*1*1
if 1 place or no place contain one that is in 4*3*2 ways
so total 1+9+24=34 ways is possible

Is this solution Helpfull? Yes (1) | No   

Madhavi Mokkapati  (10 years ago)

Condition will collide,

For first place, any of the 4 numbers i.e., 4ways
For 2nd place, any of 4 numbers i.e., 4ways and
1.) if it takes digit '1' then for 3rd place any of 4 numbers(1 repition is allowed) i.e., 4ways
2.) if it takes any other digit, then for 3rd place any of 3 numbers i.e., 3ways

add the cases,

4*4*4+4*4*3=112

Is this solution Helpfull? Yes | No (3)  

Mani kandan  (10 years ago)

can Any 1 explain how 3 digit numbers can be formed using 1,2,3,4.
what is 1 number can be repeated.,then how?

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mekala  (9 years ago)

first digit never comes 0 =3,2nd digit=4 and 3rd=4-2=2,so ways are 3*4*2=24

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