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CBSE Class 12-science Answered

From a bag containing 8 white and 5 Black balls. Four balls are drawn one by one without replacement . Find the probability that exactly two of them are white.

Asked by sachinkumarmishra1 | 23 Jan, 2020, 12:00: PM
Expert Answer
Total number of balls = 8+5 = 13
4 balls are drawn at random out of which exactly two balls are white, so the remaining two balls are black
1st ball can be drawn in 13C1 no. of ways
Only 12 balls are left, so the 2nd ball can be drawn in 12C1 no. of ways
Only 11 balls are left, so the 3rd ball can be drawn in 11C1 no. of ways
Only 10 balls are left, so the 4th ball can be drawn in 10C1 no. of ways
So, the total number of ways of drawing 4 balls = 13C112C111C110C1
No of ways such that exactly 2 balls are white = 8C1 x 7C1
No of ways such that exactly 2 balls are black = 5C1 x 4C1
The space balls space can space be space arranged space in space fraction numerator 4 factorial over denominator 2 factorial space 2 factorial end fraction space no. of space ways space among space themselves
therefore space Required space probability equals fraction numerator straight C presubscript 1 presuperscript 8 space cross times space straight C presubscript 1 presuperscript 7 space cross times space straight C presubscript 1 presuperscript 5 space cross times space straight C presubscript 1 presuperscript 4 over denominator straight C presubscript 1 presuperscript 13 cross times straight C presubscript 1 presuperscript 12 cross times straight C presubscript 1 presuperscript 11 cross times straight C presubscript 1 presuperscript 10 end fraction cross times fraction numerator 4 factorial over denominator 2 factorial space 2 factorial end fraction equals fraction numerator 8 cross times 7 cross times 5 cross times 4 over denominator 13 cross times 12 cross times 11 cross times 10 end fraction cross times 6 equals 56 over 143
Answered by Renu Varma | 24 Jan, 2020, 10:31: AM
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