Martin's Dance Playlist

We can count systematically, since whatever we choose to be the first song in the playlist cannot be chosen as the second, and whatever we choose for the first and second song cannot be chosen for the third. Thus, by the product rule, the number of possible ordered playlists is $24 \times (24 - 1) \times (24 - 2) = 12144,$ and the last three digits of this is $\boxed{144}$ .

permutation of 24 things taking 3 at a time. 24P3=22 23 24=12144

N = 24P3 = 12144 , so the last 3 digits of N = 144

There are 24 songs and the playlist could only have 3 songs (with orders matter). We may use permutation in this problem: 24P3=12144 Therefore, the answer to the question is 144.

The number of playlists which can be formed is: $24 \times 23 \times 22$ . Since only the last 3 digits are needed, just multiply $24 \times 3 \times 2$ and you'll get 144. ( $4 \times 3 \times 2$ doesn't give you a 3-digit answer)

We can choose $3$ songs from $24$ songs in $^{24}P_3 = 12144$

Now , $12144 \equiv \boxed {144} \pmod{100}$

Permuation is the key word.

So, $P ( 24 , 3 )$

$24 \times 23 \times 22$

They equal 12144. Answer is $144$

24P3=12144

the last three digits are 144 :)

According to the given situation, total number of songs are 24.

Martin wants to make a playlist of 3 songs where order of songs matter.

This is similar to the case when we want to select and arrange 3 objects out of 24.

$\frac{24!}{(24-3)!}$ = $\frac{24!}{22!}$ = $\mathrm{12144}$

Hence our final answer is $\fbox{144}$