Question

A bucket contains 6 blue, 8 red and 9 black pens. If six pens are drawn one by one without replacement, find the probability of getting all black pens?

(a) \(\frac{8}{213}\)

(b) \(\frac{8}{4807}\)

(c) \(\frac{5}{1204}\)

(d) \(\frac{7}{4328}\)

The question was asked in an online quiz.

I would like to ask this question from Discrete Probability topic in section Discrete Probability of Discrete Mathematics

Answer 1

Right answer is (b) \(\frac{8}{4807}\)

To explain: Total number of pens = 23, number of pens we have chosen = 6, total number of black pens = 9. According to the combination probability formula it states that ^nCr = \(\frac{n!}{r! (n-r)!}\),

where n = total number of outcomes, r = random selection, P = \(\frac{^9C_6}{^{23}C_6} = \frac{8}{4807}\).