A bag contains 4 yellow, 5 red, 3 green, 4 black balls. If 4 balls are drawn randomly without replac

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11 Mar 2022 Probability

A bag contains 4 yellow, 5 red, 3 green, 4 black balls. If 4 balls are drawn randomly without replacement, what is the probability that the balls drawn contain balls of different colours?

OPtion

1) 2/91
2) 7/26
3) 12/91
4) 1/182
5) 6/91
6) 30/91
7) 5/182
8) 24/91
9) 11/26
10) None of these

Solution

Total balls = 4+5+3+4 = 16
Number of ways 4 balls can be drawn from 16 balls = 16C4
For the 4 balls to be of different colours, we need 1 ball each of yellow, red, green and black colour.
So favourable cases = 4C1 x 5C1 x 3C1 x 4C1
Required probability = 4C1 x 5C1 x 3C1 x 4C1 / 16C4 = 240/1820 = 12/91

Correct Option: 3 Best Solution (1)

Mayank Kandoi   2 years AGO

Ways of drawing 1 yellow ball out of 4 yellow balls = (4C1) = 4
Ways of drawing 1 red ball out of 5 red balls = (5C1) = 5
Ways of drawing 1 green ball out of 3 green balls = (3C1) = 3
Ways of drawing 1 black ball out of 4 black balls = (4C1) = 4

Ways of drawing 4 balls out of 16 = (16C4) = 14*13*10

Therefore, probability of getting 4 balls of different colours from first four draws without replacement = [(4*5*3*4) / (14*13*10)] = (12 / 91)

Option 3

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