Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: · Marks: · Difficulty:
A box contains 2 white, 3 black and 4 red balls. In how many ways can 3 balls be drawn from the box, ) if at least 1 black ball is to be included in the draw?
(a)32
(b)48
(c)64
(d)96
(e)None of these
Answer
Answer (as printed): C
Explanation
We may have (1 black and 2 non-black) or (2 black and 1 non-black) or (3 black). Required no. of ways = (3C1 × 6C2) + (3C2 × 6C1) + (3C3) 6 × 5 3 × 2 = 3 × + × 6 + 1 = (45 + 18 + 1) = 64. 2 × 1 2 × 1
Explanation as extracted from the printed page; notation may be imperfect.