Hello,
The problem:
Mike's playlist contains 20 songs, including 3 from the Beatles. Determine the probability that, in random mode, two Beatles songs are played one after the other.
My reasoning:
The number of combinations for the playlist in random mode is 20 factorial, and to determine the number of combinations containing two Beatles songs in a row, I thought that there can be 19 slots for these two songs: in positions 1 and 2, 2 and 3, ... 19 and 20.
Moreover, as there are 3 Beatles songs, there are 6 pairs of 2 songs possible: AB, BA, AC, CA, BC, CB. So there are 19 x 6 = 114 possible playlists containing 2 Beatles songs in a row on a total of 20! possible playlists. So, the probability we are looking for is [MATH]\frac{114}{20!} [/MATH].
Is it correct ?
The problem:
Mike's playlist contains 20 songs, including 3 from the Beatles. Determine the probability that, in random mode, two Beatles songs are played one after the other.
My reasoning:
The number of combinations for the playlist in random mode is 20 factorial, and to determine the number of combinations containing two Beatles songs in a row, I thought that there can be 19 slots for these two songs: in positions 1 and 2, 2 and 3, ... 19 and 20.
Moreover, as there are 3 Beatles songs, there are 6 pairs of 2 songs possible: AB, BA, AC, CA, BC, CB. So there are 19 x 6 = 114 possible playlists containing 2 Beatles songs in a row on a total of 20! possible playlists. So, the probability we are looking for is [MATH]\frac{114}{20!} [/MATH].
Is it correct ?