Latest UPSC Aptitude Question SOLUTION: how many three digit numbers can generated from 1,2,3,4,5,6,7,8,9 such that the digits are in ascending order. 1)80 2)81 3)83 4)84

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(#M40013762) UPSC HR Interview question Keep an EYE

how many three digit numbers can generated from 1,2,3,4,5,6,7,8,9 such that the digits are in ascending order.
1)80
2)81
3)83
4)84

Asked In UPSC keshav (11 years ago)

Unsolved Read Solution (8)

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Read Solution (8) :

Garima  (11 years ago)

84

Number of Numbers starting with 1 = 7+6+5+..+2+1=28
Number of Numbers starting with 2 = 6+5+..+2+1=21
Number of Numbers starting with 3= 5+..+2+1=15
..
..
Number of Numbers starting with 7 = 1

Total three digit numbers that can generated from 1,2,3,4,5,6,7,8,9 such that the digits are in ascending order = 28+21+15+10+6+3+1 = 84

Is this solution Helpfull? Yes (10) | No (2)  

apurva mishra  (9 years ago)

9*8*7/3!=84
Possible numbers=84

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

Stoycho  (9 years ago)

4)84
9*8*7/3!=504/6=84

Is this solution Helpfull? Yes | No (2)  

Rohan  (8 years ago)

Numbers starting with 1 will be 28....
with 2 will be 21
with 3 will be 15
with 4 will be 10
with 5 will be 6
with 6 will be 3
with 7 will be 1......so the total 84

Is this solution Helpfull? Yes | No (2)  

Akash  (8 years ago)

84 9c3..
Already ascending

Is this solution Helpfull? Yes | No (1)  

tejaswi A  (7 years ago)

ans-4)84
count of numbers starting with 1:-7+6+5+4+3+2+1
{7=count of numbers starting with 12
6=count of numbers starting with 13
5=count of numbers starting with 14
.
.
.
}
count of numbers starting with 2:-6+5+4+3+2+1
count of numbers starting with 3:-5+4+3+2+1
count of numbers starting with 4:-4+3+2+1
count of numbers starting with 5:-3+2+1
count of numbers starting with 6:-2+1
count of numbers starting with 7:1

hence the total count is 84

Is this solution Helpfull? Yes | No   

MADHUBALA  (7 years ago)

9c3=9*8*7/1*2*3
=84
ANS:84

Is this solution Helpfull? Yes | No   

gaurav  (6 years ago)

first place 1 second vary from 2 to 8 and third vari from 3 to 9 total=28
similary first place 2 second vary form 3 to 8 and third vary form 4 to 9 =21
15
10
6
3
1
total 28+21+15+10+6+3+1=84

Is this solution Helpfull? Yes | No   

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