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Original Question
A coordinator will select 4 songs from a list of 14 songs to compose an event's musical entertainment lineup. How many differen...Question
A coordinator will select 5
songs from a list of 7
songs to compose an event's musical entertainment lineup. How many different lineups are possible?
songs from a list of 7
songs to compose an event's musical entertainment lineup. How many different lineups are possible?
Answers
Answered by
GPT 3.5
To calculate the number of different lineups possible, we can use the combination formula.
The formula for combination is:
nCr = n! / [r!(n-r)!]
Where n is the total number of songs (7) and r is the number of songs to be selected (5).
Plugging in the values, we get:
7C5 = 7! / [5!(7-5)!]
7C5 = 7! / [5!*2!]
7C5 = (7*6*5*4*3*2*1) / [(5*4*3*2*1)*(2*1)]
7C5 = 5040 / (120*2)
7C5 = 5040 / 240
7C5 = 21
Therefore, there are 21 different lineups possible for the event's musical entertainment.
The formula for combination is:
nCr = n! / [r!(n-r)!]
Where n is the total number of songs (7) and r is the number of songs to be selected (5).
Plugging in the values, we get:
7C5 = 7! / [5!(7-5)!]
7C5 = 7! / [5!*2!]
7C5 = (7*6*5*4*3*2*1) / [(5*4*3*2*1)*(2*1)]
7C5 = 5040 / (120*2)
7C5 = 5040 / 240
7C5 = 21
Therefore, there are 21 different lineups possible for the event's musical entertainment.