Question

6.On Saturday, Jane likes to work out, eat, and read a book. She will either lift weights, run, or hike. Then she will choose 1 of the 6 restaurants near her home, and read either Harry Potter, Catcher in the Rye, or Girl on the Train. How many different ways can she spend her Saturday?

Answer 1

Number of different ways can she spend her Saturday = 54

Explanation:

Jane has to do three types of things - Work out , Eat and Read a book

In Work out -

She either lift weights, run, or hike

In Eating -

She will choose 1 of the 6 restaurants near her home

In Reading -

Read either Harry Potter, Catcher in the Rye, or Girl on the Train

Number of ways in which she can work put = ³C₁ =
`(3!)/(1! (3-1)!) = (3!)/(2!) = 3`

Number of ways in which she can eat = ⁶C₁ =
`(6!)/(1! (6-1)!) = (6!)/(5!) = 6`

Number of ways in which she can read = ³C₁ =
`(3!)/(1! (3-1)!) = (3!)/(2!) = 3`

So, Total number of ways = 3×6×3 = 54