Latest TCS Aptitude Question SOLUTION: How many positive integers less than 500 can be formed using the numbers 1,2,3,and 5 for digits, each digit being used only once.

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How many positive integers less than 500 can be formed using the numbers 1,2,3,and 5 for digits, each digit being used only once.

Asked In TCS Trbeni (10 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

saima kidwai  (10 years ago)

3 digits no formed= 3*3*2 (5 cant come at place,no should be less than 500)
=18
2 digit no formed=4*3
=12
1 digit no formed=4
total positive integers=18+12+4
=34

Is this solution Helpfull? Yes (90) | No (15)  

Priyanka Ganguly  (10 years ago)

34
exp:
one digit nos=4
two digit nos=4c2
three digit nos which starts with 1 is 6
three digit nos which starts with 2 is 6
three digit nos which starts with 3 is 6
so total 4+12+18

Is this solution Helpfull? Yes (15) | No (10)  

sandy  (10 years ago)

let us consider _ _ _(3 digit num).
as it is given that the nums should be less than 500 so we shouls not use 5 in 100's place
out of 3 (1,2,3) 100's place can be filled by one num in 3c1 ways=3
out of 3 remaining 10's place can be filled by one num in 3c1 ways=3
out of 2 remaining 1's place can be filled in 2c1 ways=2
therefore no of ways=3*3*2=18ways

Is this solution Helpfull? Yes (13) | No (10)  

pavan kumar  (10 years ago)

@priyanka:4c2=6 know?

Is this solution Helpfull? Yes (7) | No (7)  

Lalit Chandrakant Deshmukh  (7 years ago)

FOR SINGLE DIGIT NO.=4 WAYS
FOR DOUBLE DIGIT NO.= 4! WAYS
FOR THREE DIGIT NO. 3! WAYS
4+4!+3!=34

Is this solution Helpfull? Yes (6) | No   

Raushan Kumar  (10 years ago)

when 5 is placed at 100th position,total combination=3!
without any restriction=3!
so,less than 500=4!-3!=18 ways.

Is this solution Helpfull? Yes (4) | No (11)  

AnushO  (9 years ago)

Ans=34
Single digit numbers = 4
Double digit numbers = 4 x 3 = 12
Three digit numbers = 3 x 3 x 2 x 1 = 18
Total = 4+12+18=34

Is this solution Helpfull? Yes (4) | No (7)  

Nikhil kumar jha  (8 years ago)

34

one digit nos=4
two digit nos=4c1*3c1=12
three digit nos which starts with 1 is 6
three digit nos which starts with 2 is 6
three digit nos which starts with 3 is 6
so total 4+12+18

Is this solution Helpfull? Yes (3) | No   

Arti Pawar  (7 years ago)

1 digit numbers= (4!)/(3!)= 4;
2 digit numbers= (4!)/(2!)= 12;
3 digit numbers= (4!)/(1!)= 24; but 512, 513, 521, 523, 531, 532 these 6 numbers are greater than 500, so 24-6= 18;
So that answer is 18+12+4= 34.

Is this solution Helpfull? Yes (3) | No   

Prasanjeit Biswas  (9 years ago)

3 digits number can be formed by
3*3*2 ways since 5 cannot be the first digit
so 18
No two digit or three digit number can be formed because there is no 0 in the digit list

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

neha upadhyay  (7 years ago)

Single digit number = 4
Double digit number = 4××3 = 12
Three digit numbers = 3××3××2= 18 (∵∵ If Hundred's place is 5, then the number is greater than 500)
Total = 34.

Is this solution Helpfull? Yes (1) | No   

naveena  (7 years ago)

Possible ways
1 digit => 4
2 digit=>4*3=12
3 digit=>3*3*2=18
total=4+12+18=34

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

sarathkumar  (9 years ago)

possible numbers are ly 18 try to put all numbers like 123 125 ,...upto.352

Is this solution Helpfull? Yes | No (3)  

Mradul Singh  (4 years ago)

4+12+24=40

Is this solution Helpfull? Yes | No   

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