M4maths Previous Puzzles

13 Aug 2015 Permutation combination

There is a 3 digit positive number such that sum of all its digits is equal to 6. How many such number are possible.

OPtion

1) 13
2) 15
3) 16
4) 17
5) 18
6) 19
7) 20
8) 21
9) 22
10) 23

Solution

Total numbers using
6,0,0 = 1�2!/2! = 1
5,1,0 = 2 � 2! = 4
4,2,0 = 2 � 2! = 4
4,1,1 = 3!/2! = 3
3,2,1 = 3! = 6
3,3,0 = 1 � 2! = 2
2,2,2 = 1
So total numbers = 21

Correct Option: 8 Best Solution (7)

Rahul kumar   9 years AGO

105
114
123
132
141
150
204
213
222
231
240
303
312
321
330
402
411
420
501
510
600
total 21 nos having sum =6

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Sushmita Ghanty   9 years AGO

3 digit positive numbers such that sum of all its digits is equal to 6 are:
600
114,141,411
123,132,213,231,312,321
510,501,105,150
420,402,240,204
330,303
222
total possible number is: 21

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Deepak kumar kumawat   9 years AGO

there is 21 such numbers
105
114
123
132
141
150...........................6
204
213
222
231
240...............................5
303
312
321
330......................4
402
411
420....................3
501
510....................2
600....................1
hence total=6+5+4+3+2+1=21

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Narendra Gopi   9 years AGO

starting with1 105,114,123,132,141,150
starting with 2 204,213,222,231,240
starting with 3 303,312,321,330
starting with 4 402,411,420
starting with 5 501,510
starting with 6 600
total 21 numbers.

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Math Lovers   9 years AGO

The sum of 3 digit number is 6 so digit can be from 0 to 6.

Now See the possibilities -
600 -> 1 number
501 -> 4 number (501, 510, 105, 150)
402 -> 4 number (402, 420, 204, 240)
303 -> 2 number (303, 330)
113 -> 3 number (113, 131, 311)
213 -> 6 numbers (123, 132, 213, 231, 312, 321)
222 -> 1 number (222)

so total number =21

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Shweta Sharma   9 years AGO

the combinations of the no whose sum is 6 are
~150= 3!-2 number= 4 (2 subracted for 015 and 051)
~141=3!/2! number= 3
~132=3! number=6
~222= 1 number=1
~240=6!-2 number=4 (2 for 024 and 042)
~330=2 number (ie 330 and 303)
~600= 1 number
total=4+3+6+1+4+2+1=21 number

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velmala gangadhar   9 years AGO

105 204 303
114 213 312 402 501 600
123 222 321 411 510
132 231 330 420
141 240
150
6+5+4+3+2+1=21

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