Question

In how many ways can Tim draw a red or a green marble from a jar containing 20 red marbles and 4 green marbles?

Answer 1

I believe the answer is 24

Answer 2

The number of ways we can choose from n objects picking r at a time is given by the formula;

$nC_r = \frac{n ! }{(n - r) ! r ! }$

Number of ways Tim can draw 1 red marble from 20 red marbles is

$20C_1 = \frac{20! }{(20 - 1) ! 1 ! } = \frac{20 \times 19 ! }{19 ! 1! } = 20$

Number of ways Tim can draw 1 green marble from 4 green marbles is

$4C_1 = \frac{4! }{(4 - 1) ! 1 ! } = \frac{4 \times 3 ! }{3 ! 1! } = 4$

Number of ways Tim can draw a red or green marble is

$20C_1 +4C_1 = 20 + 4 = 24$

Hence the correct answer is 24.