Answer: The required number of different groups is 32468436 and it is calculated by the number of combinations because position of songs does not matter.
Step-by-step explanation: Given that Sean has 56 songs on his MP3 player and he wants to randomly select 6 of the songs to use in a school project.
We are to find the number of different groups of 6 songs that could Sean select.
Since Sean needs 6 different groups of songs, so the position of the songs do not matter. That is, we will use combination here.
Therefore, the number of different groups of 6 songs is
[tex]^{56}C_6=\dfrac{56!}{6!(56-6)!}=\dfrac{56\times55\times54\times53\times52\times50}{6\times5\times4\times3\times2\times1}=32468436.[/tex]
Thus, the required number of different groups is 32468436 and it is calculated by the number of combinations because position of songs does not matter.
