Aptitude - Permutation and Combination - Discussion
Discussion Forum : Permutation and Combination - General Questions (Q.No. 9)
9.
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
Answer: Option
Explanation:
We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).
 Required number of ways |
= (3C1 x 6C2) + (3C2 x 6C1) + (3C3) | |||||||||||||
|
||||||||||||||
| = (45 + 18 + 1) | ||||||||||||||
| = 64. |
Discussion:
81 comments Page 5 of 9.
Chiru said:
9 years ago
It's simple.
The combination of all balls - neglecting combination of remaining balls (except at least one ball) = at least one black.
9c3 - 6c3 = 64.
The combination of all balls - neglecting combination of remaining balls (except at least one ball) = at least one black.
9c3 - 6c3 = 64.
RupamRD said:
9 years ago
2 White balls (W)
3 black balls (B)
4 red balls (R)
1W 1R 1B : (2c1 * 3c1 * 4c1)
1W 2B : (2c1 * 3c2)
1R 2B : (4c1 * 3c2)
2W 1B : (2c2 * 3c1)
2R 1B : (4c2 * 3c1)
3B + (3c3)
_______
64
_______
3 black balls (B)
4 red balls (R)
1W 1R 1B : (2c1 * 3c1 * 4c1)
1W 2B : (2c1 * 3c2)
1R 2B : (4c1 * 3c2)
2W 1B : (2c2 * 3c1)
2R 1B : (4c2 * 3c1)
3B + (3c3)
_______
64
_______
Viren Lakum said:
9 years ago
There are 9 balls in box, and as given one of them has to be black so we get,
(1 black and any 2) + (2 black and any 1) + ( 3 black)
(3C1 x 8C2) + (3C2 x 7C1) + (3C3) = 168 + 21 + 3 = 192.
(1 black and any 2) + (2 black and any 1) + ( 3 black)
(3C1 x 8C2) + (3C2 x 7C1) + (3C3) = 168 + 21 + 3 = 192.
Mitali said:
9 years ago
If we consider that the balls are not identical, then one black ball for sure can be selected in 3C1 ways, after that, you can select any 2 out of the remaining 8 in 8C2, which will include black also. Can someone explain why this 3C1 x 8C2 also equals the total number of ways of selecting 3 balls out of 9 (i.e. 9C3)?
Anil said:
9 years ago
Can anybody tell me why the answer is not 3C1 x 8C2 = 84?
(1)
Gauss said:
9 years ago
Can anybody tell me why the answer is not 3C1 x 8C2 = 84?
Apluv said:
9 years ago
Answer is 64. If the colors are different then balls are not identical.
Naveen said:
9 years ago
@Pavel Sain: Since the ball of the same colour are identical, you should do ((3C1/3!) * (2C1/2!) * (4C1/4!)) etc.
So either you use the formula or make the individual combinations, the answer will be 6.
So either you use the formula or make the individual combinations, the answer will be 6.
Revathy said:
9 years ago
I think Pavel Sain's answer is correct.
Himanshu Kulkarni said:
9 years ago
One black ball from 3 is 3C1 and any 2 balls from remaining 8 balls
i.e. 8C2.
So, why 3C1 x 8C2 does not match the solution?
i.e. 8C2.
So, why 3C1 x 8C2 does not match the solution?
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers