A doctor's office has 8 openings each day. If only 5 people are scheduled with the...

A doctor's office has 8 openings each day. If only 5 people are scheduled with the doctor today:

a) How many ways can the 5 appointments be arranged in the available times?

b) why did you choose the strategy you did

c) this doctor prefers to sleep in. How many ways can the appointments be arranged with the first two morning openings left empty?

d) what is the probability of the first twi appointment slots being left empty by chance if the 5 appointments are scheduled randomly?

Solutions

Expert Solution

a) How many ways can the 5 appointments be arranged in the available times?

We need to place 5 appointments in 8 slots, here the order in the which the appointments are placed does matter. Hence we use premutation.

b) why did you choose the strategy you did

We need to place 5 appointments in 8 slots, here the order in the which the appointments are placed does matter. Hence we use permutation.

c) this doctor prefers to sleep in. How many ways can the appointments be arranged with the first two morning openings left empty?

Now the first two slots are not available. Hence 5 appointments must be placed in 5 slots.

d) what is the probability of the first twi appointment slots being left empty by chance if the 5 appointments are scheduled randomly?

Probability = (Ways in which appointment are placed in 5 slots) / (Total number of ways)= 120/6720 = 0.017857143

orchestra answered 1 year ago

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