Problem Solving

q: a jar contains only red, yellow and orange marbles. If there are 3 red, 5 yellow and 4 orange marbles and 3 marbles are selected at randm without replacing any of them, whats the probabbility that 2 yellow, 1 red and no orange marbles will be chosen
A) 1/60
1/45
2/45
3/22 ans
5/22

Total possibilities to choose 3 marbles: 12C3 = 220
Possibilities to choose 2 yellow: 5C2 = 10
Possibilities to choose 1 red: 3C1 = 3
Possibilities to choose 0 orange: 4C0 = 1

Probability = desired # of possibilities for your outcome / total possibilities = (10 * 3 * 1) / 220 = 30 / 220 = 3/22. Choice D.

you can alternatively solve this using the following method

we can choose

yellow, yellow, red
yellow, red, yellow
red, yellow, yellow

so,
5/12 * 4/11 * 3/10 [ 5 out of 12 yellow, remaining 4 yellow out of 11, 3 red out of 10 ]
+
5/12* 3/11 * 4/10 [ 5 out of 12 yellow, 3 red out of remaining 11 balls, 4 yellow out of remaining 10 balls ]
+
3/12 * 5/11 * 4/10 [ on similar grounds , choose red, yellow, yellow .]

we get
3/22

~Nik