• Numerical Ability - Permutation & Combination Or Probability
Question

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

  • A) 2/91
  • B) 1/22
  • C) 3/22
  • D) 2/77
  • E) None of these
Solution

Let S be the sample space.

Then, n(S) = number of ways of drawing 3 balls out of 15 = 15C315C3  =15*14*133*2*115*14*133*2*1= 455.  

Let E = event of getting all the 3 red balls.

 n(E) = 5C35C3 = 5*42*15*42*1 = 10.

 => P(E) = n(E)/n(S) = 10/455 = 2/91.

Let S be the sample space.

Then, n(S) = number of ways of drawing 3 balls out of 15 = 15C315C3  =15*14*133*2*115*14*133*2*1= 455.  

Let E = event of getting all the 3 red balls.

 n(E) = 5C35C3 = 5*42*15*42*1 = 10.

 => P(E) = n(E)/n(S) = 10/455 = 2/91.
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