There are 8 programs in the New Year's Gala, including 3 non-singing programs. When arranging the program list, it is stipulated that non-singing programs are not adjacent, and the first and last programs are singing programs. How many different arrangement methods are there in the playlist?
新年联欢会共有8个节目，其中有3个非歌唱类节目．排列节目单时规定，非歌唱类节目不相邻，而且第一个和最后一个节目是歌唱类节目．则节目单有多少种不同的排法．
<gadget id="calculator">5 * 4 * 3 * 2 * 1</gadget>
<output>120</output>

<gadget id="calculator">4 * 3 * 2</gadget>
<output>24</output>

<gadget id="calculator">120 * 24</gadget>
<output>2_880</output>

<result>2_880</result>