There are 5 cylinders 5 cubes and 5 pyramids Sandra randomly

There are 5 cylinders, 5 cubes, and 5 pyramids. Sandra randomly chooses two shapes from the set at the same time. What is the probability that one shape is a cube or a pyramid?

Solution

Solution : totally there are 15 shapes , number of ways of selecting 2 shapes = 15C ₂ ( total outcomes)

= 15 x 14 / 2 105

Number of ways of selecing 2 cubes = 5 C₂ = 5x4 /2 =10. no of ways of selecting 2 pyramid = 5C₂ ,=10

No of ways of selecting 1 cube or 1 pyramid = 5C₁X5C₁ = 5 x 5 =25

No of ways of selecting one sshape is a cube or pyramid = 10+10+25=45 (favourable outcomes)

requored probability = No of favourable outcomes / total outcomes = 45 / 105 = 3 / 7