Question

Choose the appropriate counting technique and answer the question. Your personal trainer is trying to design...

Choose the appropriate counting technique and answer the question. Your personal trainer is trying to design a work out for you. There are 20 possible exercises to choose from and they want you to do 4 each day, but you know that there would be a huge difference what order you had to do them in. How many possible work outs could your trainer design?

Math   Statistics-And-Probability   
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Answer #1

For day 1:

Number of ways of selecting 4 works for day 1 is C(20,4). Then number of possible order of workouts is 4!. So possible order of work out for day 1 is

C(20,4) * 4!

For day 2:

Number of ways of selecting 4 works for day 2 is C(16,4). Then number of possible order of workouts is 4!. So possible order of work out for day 2 is

C(16,4) * 4!

Likewise for day 3, day 4 and day 5 possible order of workouts are C(12,4) * 4! , C(8,4) * 4! and C(4,4) * 4! respectively.

So required possible order of work out is

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