If x+y+z = 9; then probability of having x = y = z = 3 will be, x, y, z are positive integers

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29 May 2015 Probability

If x+y+z = 9; then probability of having x = y = z = 3 will be, x, y, z are positive integers

OPtion

1) 1/28
2) 1/7
3) 1/14
4) 1/6
5) 1/3
6) 1/2
7) 1/16
8) 1/10
9) 1/8
10)1/56

Solution

For x = 1, y and z can be arranged in 7 ways
for x = 2, y and z can be arranged in 6 ways
for x = 3, y and z can be arranged in 5 ways
Similarly
------------
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for x = 7, y and z can be arranged in 1 ways
Total ways = 7+6+5+4+3+2+1 = 28
So probability 1/28
Option 1)

Correct Option: 1 Best Solution (14)

Radhika   9 years AGO

the total of x+y+z=9. therefore, the combinations of values of x,y,z will be
1,3,5 can be arranged in 3! ways=6
1,2,6 can be arranged in 3! ways=6
2,3,4 can be arranged in 3! ways=6
1,1,7 can be arranged in 3 ways=3
1,4,4 can be arranged in 3 ways=3
2,2,5 can be arranged in 3 ways=3
Now, 3,3,3 can be arranged in 1 way=1
The total combinations are = 6+6+6+3+3+3+1=28
therefore, the probability of getting (x=y=z=3) = 1/28

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W J Krishna Teja   9 years AGO

required probability=3/9c3

Like? Yes (1) | No   

Karthick Raja   9 years AGO

Total possibilities is 28
so probability is 1/28
117,126,135,145,154153,162,171
216,225,234,243,252,261
315,324,333,343,351
414,423,432,441
513,522,531
612,621
711

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vivek   9 years AGO

total no of outcomes = 28
required probability is 1/28

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Vaibhav Srivastava   9 years AGO

Favorable case = 1
Sample space = 28

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ravi singh   9 years AGO

answer is 1/28
total possible conditions are 28 because zero is neither positive nor negative,
hence probability = 1/28

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Mehul D Parmar   9 years AGO

because x=y=z=3 is possible only one time from 28 cases.here favourable case is 1 and total case is 28 than 1/28 is right ans.


here , give positive integers if non negative integers than find dircectly

n+r-1 9+3-1
c = c
r-1 3-1


bt here positive integer than find manually.

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anubhav verma   9 years AGO

number of combination with 7
with 2. 6 and so on
therefore number of combination with 7 at hundereds place are 1
total number of combination made is 28 and all three be equal to 3 is one combination of it hence 1:28

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keerthi   9 years AGO

they gave eq x+y+z=9 i.e., either x=9 or y=9 or z=9 so that in denominator we can write it as 9*9*9

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Abdullah khan   9 years AGO

Total number of cases will be ::
x + y = z = 6 { x>=0 ,y>=0 ,z>=0 }
(6+3-1)
C (3-1) =====
8
C =================28
2
hence the probaility of x=y=z=3 is 1/28

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PRASHANT KUMAR   9 years AGO

117 216 315................... 711
126 225 324.......
135 234 333.....
. . .
. . .
. . 351
. 261
171
total terms =7+6+5+4+3+2+1=28
no. of favourable terms =1 (333 only)
so P=1/28

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vibhu raj gupta   9 years AGO

total favorable cases 28
probability=1/28

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Paresh   9 years AGO

117 126 135 144 162 153 171
216 225 234 243 252 261
315 324 333 342 351
414 423 432 441
513 522 531
612 621
711

option 1

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vivek raj   9 years AGO

total outcomes
7/1/1-3
6/2/1-6
5/2/2-3
5/3/1-6
4/3/2-6
4/1/4-3
3/3/3-1

=28
favorable outcome 3/3/3=1

1/28

Like? Yes (1) | No (3)