A box contains 6 red, 4 blue, 2 green and 4 yellow pens. If four pens are picked at random, what is the probability that one is green, two are blue and one is red?

Explanation

Total number of pens = 6 + 4 + 2 + 4 = 16 Let S be the sample space. Then, n(S) = number of ways of drawing 4 pens out of 16 = ¹⁶C4 = (16 × 15× 14 × 13 )/( 4 × 3 × 2 × 1) = 1820 Let E= event of drawing 4 pens so that one is green, two are blue and one is red = n(E) = ²C1×⁴C2×⁶C1= 2 × 6 × 6= 72 ∴ P (E) = (n(E))/(n(S))= 72/1820 = 18/455