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?

Answer 1

[AI-generated answer — Bot 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.