Icas results are out online, and only 20% answered this problem, which seems relatively easy at first, correctly:
Mary had 3 identical cubes. each cube has one pink face and one yellow face. the rest of the faces were blue. she joined the cubes as shown to form a solid (3 cubes connected in a line). what is the probability that the faces on the Bottom of the solid have 3 different colours.
the first thing I thought was 3! x 1/6 x 1/6 x 4/6 = 1/9
3! for the no. of ways the colours can be arranged
1/6 for the probability that yellow and pink are at the bottom
4/6 for the probability that blue is at the bottom.
but the correct answer is 7/48 ?? an explanation would be greatly appreciated.
Mary had 3 identical cubes. each cube has one pink face and one yellow face. the rest of the faces were blue. she joined the cubes as shown to form a solid (3 cubes connected in a line). what is the probability that the faces on the Bottom of the solid have 3 different colours.
the first thing I thought was 3! x 1/6 x 1/6 x 4/6 = 1/9
3! for the no. of ways the colours can be arranged
1/6 for the probability that yellow and pink are at the bottom
4/6 for the probability that blue is at the bottom.
but the correct answer is 7/48 ?? an explanation would be greatly appreciated.