x + y + z = 6, where x, y, z are integers from 0 to 6, Total no. of possible set of values of x,

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23 Apr 2010 Possible set of x,y,z

x + y + z = 6, where x, y, z are integers from 0 to 6,
Total no. of possible set of values of x, y and z are ?

OPtion

1) 28
2) 27
3) 24
4) 21
5) 20
6) 18
7) 16
8) 30
9) 36
10) 35

Solution

Formula for solving problem = (n+r-1) (n+r-2)/(r-1) (r-2)
Here n = 6 & r = 3
On applying values we get (6+3-1) (6+3-2) / (3-1) (3-2) = 8*7/2*1 = 28

Correct Option: 1 Best Solution (11)

sanjib biswas   14 years AGO

total possible set of values of x,y,z is 7+6+5+4+3+2+1=7*8/2=28

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HARMEET KAUR   14 years AGO

Total sets = 7+6+5+4+3+2+1= 28

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S. Singh   14 years AGO

when x=6, y=0,z=0... one set
when x=5, y=0/1, z= 1/0 ... 2 sets
when x=4, y= 0/1/2, z= 2/1/0.. 3 sets
.. similarly for all values of x.

Total sets = 1+2+3+4+5+6+7=28

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SUDESHNA SEN   14 years AGO

All of x, y and z can take values from 0 to 6.
Therefore, if we fix the value of any one of them, suppose of x to 0, then we have 7 combinations for the values of y and z:(0,6),(1,5),(2,4),(3,3),(4,2),(5,1),(6,0).
Similarly, if x= 1,2,3,4,5,6, then the number of combinations of values of y and z are 6,5,4,3,2,1, respectively.
Therefore, total no. of possible set of values of x, y and z are= 7+6+5+4+3+2+1= 28......Option 1)

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ASHOK ROY   14 years AGO

ll of x, y and z can take values from 0 to 6.
Therefore, if we fix the value of any one of them, suppose of x to 0, then we have 7 combinations for the values of y and z:(0,6),(1,5),(2,4),(3,3),(4,2),(5,1),(6,0).
Similarly, if x= 1,2,3,4,5,6, then the number of combinations of values of y and z are 6,5,4,3,2,1, respectively.
Therefore, total no. of possible set of values of x, y and z are= 7+6+5+4+3+2+1= 28......Option 1)

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Karthik Pandiyan   14 years AGO

combination of 6
1+5+0 >>> 6 ways
4+2+0 >>> 6 ways
3+3+0 >>> 3 ways
1+2+3 >>> 6 ways
1+1+4 >>> 3 ways
0+0+6 >>> 3 ways
2+2+2 >>> 1
totally 28 possible set of values

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Ajai U   14 years AGO

lets x=0 we can have 7 combinations for y &z
similarly when x=1 we can ve 6 combinations for y&z. and the process continues so 7+6+5+......+1=28

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Dr.Dipin Singh   14 years AGO

possible values are 006,060,015,051,024,042,033...7 sets with x=0, .
similarly 6 sets with x=1, 5 sets with x=2, 4 sets with x=3, 3 sets with x=4, 2 sets with x=5, 1 set with x=6.

...... Total sets = 7+6+5+4+3+2+1= 28

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Mihir   14 years AGO

similar to distribution of 5 oranges among 3 boys.

Here total 6 numbers in 3 parts.

possible sets = Sigma7 =28

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Khanna   14 years AGO

1+2+3+4+5+6+7=28

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Ankur Pandey   14 years AGO

8!/6!*2!

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