Answer to Question #201602 in Discrete Mathematics for sas

Question

We have 5 distinct jobs to be finished in the first 22 days of June but no two of the jobs will be finished on consecutive days. In how many ways can we plan the finishing days for these 5 distinct jobs? Write your answer: the number of ways this can be done is  

Answer 1

Because no two of the jobs will be finished on consecutive days, the number of days for finishing jobs is $N=\frac{22}{2}=11$

n=5

Number of possible ways $= \frac{N!}{n!(N-n)!}$

$=\frac{11!}{5!(11-5)!} \\ = \frac{332640}{720} =462$