Question

1. tyler has 28 songs on his computer. he is transferring eight songs to his mp3 player. this scenario represents combination. how many different ways can the songs be chosen? choose the correct answer – 28p8, 28c8, 8p28, 8c28

Explanation:

Step1: Recall combination formula

The combination formula is used when the order of selection does not matter. The number of combinations of choosing \( r \) items from \( n \) items is given by \( _nC_r=\frac{n!}{r!(n - r)!} \).

Step2: Identify \( n \) and \( r \)

Here, \( n = 28 \) (total number of songs) and \( r = 8 \) (number of songs to be chosen). Since the order of choosing songs does not matter (we are just choosing 8 songs out of 28), we use the combination formula.

Step3: Match with the options

The notation for combination of \( n \) items taken \( r \) at a time is \( _nC_r \) or \( nCr \). So for \( n = 28 \) and \( r = 8 \), it is \( _{28}C_8 \) or \( 28C8 \).

Answer:

\( 28C8 \)