From a bag containing 10 distinct balls, 6 balls are drawn simultaneously and replaced. Then 4 balls are drawn. The probability that exactly 3 balls are common to the drawings is 21 m . Then the num

Question

From a bag containing 10 distinct balls, 6 balls are drawn simultaneously and replaced. Then 4 balls are drawn. The probability that exactly 3 balls are common to the drawings is 21 m ​ . Then the numerical value of m is

TestHub · Accepted Answer

Let S be the sample space of the composite experiment of drawing 6 in the first draw and then four in second draw then ∣ S ∣ = 10 C 6 ​ × 10 C 4 ​ ​ ∴ Required probability = 10 C 6 ​ × 10 C 6 ​ 10 C 6 ​ × 6 C 3 ​ × 7 C 1 ​ ​ ​ = 10 × 9 × 8 × 7 80 × 24 ​ = 21 8 ​ ​

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