Question 1192253: A program is planned to have 4 musical numbers and 4 speeches. In how many ways can this be done if a musical number and a speech are to alternate and a musical number is to come​ first?
Answer by math_tutor2020(3817)   (Show Source):
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Consider 8 slots labeled as such
A,B,C,D
E,F,G,H
Then consider that the odd number slots A,C,E,G are for the musical numbers; while the even number slots B,D,F,H are for the speeches.
We have 4*3*2*1 = 24 ways to arrange the four musical numbers for slots A,C,E,G
Similarly, there are 4*3*2*1 = 24 ways to arrange the four speeches for slots B,D,F,H
The way I've set things up, we are guaranteed to have the order be musical number, speech, musical number, etc.
Overall, there are 24*24 = 576 ways to arrange all 8 items in this alternating pattern.
Answer: 576
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