Latest CAT Aptitude Question SOLUTION: Below there are sixteen numbers. Assuming that any three of the numbers may be drawn at random, what are the chances that three numbers will be drawn whose sum equals six? 1 2 3 1

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Below there are sixteen numbers. Assuming that any three of the numbers may be drawn at random, what are the chances that three numbers will be drawn whose sum equals six?

1 2 3 1
2 3 1 2
3 1 2 3
1 2 3 1

Asked In CAT jyotish r (12 years ago)

Solved Prerna Read Solution (8)

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Read Solution (8) :

Prerna  (12 years ago)

Either rolling '2 2 2' or some combination of '1 2 3' adds up to be 6. The chances of getting '2 2 2' are 5/16 (5 2s out of 16) times 4/15 (4 2s left out of 15) times 3/14 (3 2s left out of 14). This is 5/16 * 4/15 * 3/14 which equals 1/56.

The chances of getting some combination of '1 2 3' is equal to 6/16 (6 1s in the list) times 5/15 (5 2s out of 15 numbers left) times 5/14 (5 3s out of 14 numbers left) times the number of different combinations of '1 2 3' which is 6. This is 6/16 * 5/15 * 5/14 * 6 which equals 15/56.

1/56 + 15/56 = 16/56 or 2/7 or ~28.6%.

Is this solution Helpfull? Yes (7) | No   

Atul  (12 years ago)

29% chances are there.
detailed solution is time consuming.

Is this solution Helpfull? Yes (2) | No (4)  

Atul  (12 years ago)

out of total possible 560 combinations, 160 combinations will give sum as 6.

so % probability = 100*160/560 which is approx 29%

Is this solution Helpfull? Yes (2) | No (4)  

Vignesh  (12 years ago)

7 chances are there.

Chances that drawn three numbers sum equal six :
1,2,3 (1+2+3 = 6)
1,3,2 (1+3+2 = 6)
2,1,3 (2+1+3 = 6)
2,3,1 (2+3+1 = 6)
3,1,2 (3+1+2 = 6)
3,2,1 (3+!+2 = 6)
2,2,2 (2+2+2 = 6)

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

Vignesh  (12 years ago)

7 chances are there.

Number of 1's = 6
Number of 2's = 5
Number of 3's = 5

Chances that drawn three numbers sum equal six :
123
132
213
231
312
321

222

Is this solution Helpfull? Yes | No (2)  

jyotish r  (12 years ago)

vignesh,chances means probability. work out for probability.

Is this solution Helpfull? Yes | No (5)  

aanchal sharma  (12 years ago)

six=2,2,2 or six = 1,2,3
total number of outcomes are 16.
chances of 2,2,2 are
5/16*4/15*3/14=1/56(no repitition)
chances of 1,2,3 are
6/16*5/15*5/14*6 = 15/56
(multiply by 6, because 1,2,3 can be arranged in 6 ways.)
(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1).
total possible outcomes = 1/56 + 15/56=16/56
2/7.

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Sushil Bharati  (12 years ago)

well if the word random also means at once.. then we c t hat the probability is
15/56
which is solved by total events = (6C1 * 5C1 * 5C1 )/16C3

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