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?

80
24
16
4

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 = (n ! )/((n - r) ! r ! )`

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


`20C_1 = (20! )/((20 - 1) ! 1 ! ) = (20 * 19 ! )/(19 ! 1! ) = 20`

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


`4C_1 = (4! )/((4 - 1) ! 1 ! ) = (4 * 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.