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A bag contains 3 white, 6 black and 8 red balls. If 2 balls are drawn one by one without replacement, find the probability of getting all red balls.
1. \(\rm 6\over34\)
2. \(\rm 7\over34\)
3. \(\rm 8\over34\)
4. \(\rm 9\over34\)

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Correct Answer - Option 2 : \(\rm 7\over34\)

Concept:

  • The number of ways for selecting r from a group of n (n > r) = nCr 
  • The probability of any event to occur = \(\rm \text{The required number of cases}\over\text{Total number of cases possible}\)

Calculation:

Total number of balls = 3 + 6 + 8 = 17

Total number of red balls = 8

Selection of 2 balls out of 15 = 17C2

Selection of 2 red balls out of 5 = 8C2

So the required probability (P) = \(\rm ^{8}C_2\over^{17}C_2\)

P = \(\rm 8\times7\over17\times16\) = \(\boldsymbol{\rm 7\over34}\)

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