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Previous Year Question (PYQs)



A bag contains $6$ red and $4$ green balls. A fair die is rolled and a number of balls equal to that appearing on the die is chosen from the bag at random. The probability that all the balls selected are red is





Solution

Required probability $=\dfrac16\sum_{k=1}^6\dfrac{\binom6k}{\binom{10}k}$ Evaluating gives $\dfrac18$ Answer: $\boxed{\dfrac18}$


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