#### Answer

Makes sense.

#### Work Step by Step

The number of ways in which a series of successive things can occur is found by multiplying the number of ways in which each thing can occur.
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You would want to see in how many ways you can choose
the 1st number in the arrangement,
the 2nd number in the arrangement,
the 3rd number in the arrangement,
...
the 99th number in the arrangement,
the 100th number in the arrangement,
and, since this is a series of successive choices, you could apply the FTC.
(The answer to the first question is 100.
Each successive answer is 1 less than the previous,
and the total is
100$\times$99$\times$98$\times$...$\times$3$\times$2$\times$1=100!)
Makes sense.