Latest TCS Aptitude Question SOLUTION: what are the number of solutions for x+y+z=12, if x,y & z can take values from 1 to 7 ?

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what are the number of solutions for x+y+z=12, if x,y & z can take values from 1 to 7 ?

Asked In TCS Divya Srivastava (10 years ago)

Solved Karthika Read Solution (12)

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Read Solution (12) :

Aditya  (10 years ago)

Ans=37
if x=1, (y,z) can be (4,7)(5,6)(6,5)(7,4)
if x=2, (y,z) can be (3,7)(4,6)(5,5)(6,4)(7,3)
if x=3, (y,z) can be (2,7)(3,6)(4,5)(5,4)(6,3)(7,2)
if x=4, (y,z) can be (1,7)(2,6)(3,5)(4,4)(5,3)(6,2)(7,1)
if x=5, (y,z) can be (1,6)(2,5)(3,4)(4,3)(5,2)(6,1)
if x=6, (y,z) can be (1,5)(2,4)(3,3)(4,2)(5,1)
if x=7, (y,z) can be (1,4)(2,3)(3,2)(4,1)
Total Combination = 4+5+6+7+6+5+4=37

Is this solution Helpfull? Yes (68) | No (2)  

Karthika  (10 years ago)

Sorry I was wrong.Its 37 ways..
Possiblities are
1 4 7
1 5 6
2 3 7
2 4 6
3 4 5
2 5 5
3 3 6
4 4 4

These 7 cases will add up to 12.

Btw take the first case 1 4 7
x=1 y=4 z=7
x=1 y=7 z=4
x=4 y=1 z=7
x=4 y=7 z=1
x=7 y=4 z=1
x=7 y=1 z=4
Thus for the first case, 6 permutations are possible..

for the first 5 cases , 6*5 =30 permutations are possible.

But for 3 3 6 and 2 5 5 repetition is there. (3!/2!)*2 = 6

And for 4 4 4, 1 permutation.

So
30+6+1=37

Is this solution Helpfull? Yes (10) | No (3)  

Divya Srivastava  (10 years ago)

The correct answer is 37.

Is this solution Helpfull? Yes (4) | No (1)  

Karthika  (10 years ago)

I think 42 ways.. I couldn't solve in any easy method.
Possiblities are
1 4 7
1 5 6
2 3 7
2 4 6
2 5 5
3 3 6
3 4 5

These 7 cases will add up to 12.

Btw take the first case 1 4 7
x=1 y=4 z=7
x=1 y=7 z=4
x=4 y=1 z=7
x=4 y=7 z=1
x=7 y=4 z=1
x=7 y=1 z=4
Thus for the first case, 6 permutations are possible..
we have 7 cases,so 6*7=42

Is this solution Helpfull? Yes (3) | No (15)  

Ishan  (10 years ago)

I made a mistake...37 is correct answer

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

dedeepya chowdary  (10 years ago)

we can write as 7+4+1/7+3+2 smilarly we can write n get 9 solutn

Is this solution Helpfull? Yes | No (7)  

Avinash Aryan  (10 years ago)

12+3-1 C 12=91.

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Prakash Singh  (10 years ago)

43 solutions are possible

Is this solution Helpfull? Yes | No (12)  

Ishan  (10 years ago)

(1,4,7)---->can be arranged in 6 ways to give a solution
(1,5,6)---->can be arranged in 6 ways to give a solution
(2,3,7)---->can be arranged in 6 ways to give a solution
(2,4,6)---->can be arranged in 6 ways to give a solution
(2,5,5)---->can be arranged in 3 ways to give a solution
(3,3,6)---->can be arranged in 3 ways to give a solution
(3,4,5)---->can be arranged in 6 ways to give a solution
(4,4,4)---->can be arranged in 1 way to give a solution
(5,5,2)---->can be arranged in 3 ways to give a solution

Total no of ways= 40

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Prakash Singh  (10 years ago)

sorry for previous answer it will be 37

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Rudra  (10 years ago)

@KARTHIKA why didnt u take 5 5 2???

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Karthika  (10 years ago)

@Rudra:
x=2 y=5 z=5
x=5 y=5 z=2
x=5 y=2 z=5
these are the three ways...
So I just tuk 2 5 5 and did permutation. i.e 3!/2!=3ways as mentioned in detail above (Dividing by 2!,because "5" is repeated two times)
Rudra hope yu understud

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