Sum of 3 non zero positive integers x, y, z is 8. Total no of possible sets for the values of x, y a

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18 Mar 2011 Permutations

Sum of 3 non zero positive integers x, y, z is 8. Total no of possible sets for the values of x, y and z are

OPtion

1) 12
2) 15
3) 16
4) 18
5) 20
6) 21
7) 24
8) 25
9) 27
10) 28

Solution

Short cut
Possible values for x are (1, 2, 3, 4, 5, 6), similarly for y and z.
Minimum value of every integer will be 1, so we have to distribute remaining 5(p) to the 3(q) integers.
so answer will be (p+1).(p+2)...upto (q-1) terms/1.2...upto (q-1) terms
= 6.7/1.2 = 21

Correct Option: 6 Best Solution (6)

YadeeshKumar   13 years AGO

6+5+4+3+2+1=21

Like? Yes (9) | No (2)  

Karthick Babu   13 years AGO

1) 1,1,6
2) 1,2,5
3) 1,3,4
4) 1,4,3
5) 1,5,2
6) 1,6,1
7) 2,1,5
8) 2,2,4
9) 2,3,3
10) 2,4,2
11) 2,5,1
12) 3,1,4
13) 3,2,3
14) 3,3,2
15) 3,4,1
16) 4,1,3
17) 4,2,2
18) 4,3,1
19) 5,1,2
20) 5,2,1
21) 6,1,1
Total 21 possibilities...So ans is Option 6.

Like? Yes (6) | No (1)  

RajiniRaja S   13 years AGO

from 1 to 6 makes, sum of 3 nums=8
so the combination so the total possible sets are 6+5+4+3+2+1 =21

so the option 6 is correct.

Like? Yes (5) | No   

Balakumaran N.A   13 years AGO

1,1,6;1,2,5; like that its going on up to 21 set.

Like? Yes (5) | No (1)  

Murthy Ch.v.v.s.s.s.   13 years AGO

If we fix x=1, then y&z can be any no between 1to6. so there are 6 Options.
Similarly, if x=2, then Y&Z can be between 1 to5. so there are 5 Options
if x=3, then 4 options
if x=4, then 3 options
if x=5, then 2 options
if x=6, then 1 option
so total options = 6+5+4+3+2+1 =21

Like? Yes (4) | No   

raghunath reddy   13 years AGO

min val of x, y , z are 1.
so, we have to distribute the value 8 to three no.
so there are 7c2 ways
7c2=21

Like? Yes (4) | No