A band knows how to play 10 different songs. How many different 2-song set lists could the band perform at their next concert?
Question
A band knows how to play 10 different songs. How many different 2-song set lists could the band perform at their next concert?
Solution
This is a problem of combinations. The band has 10 songs and they want to choose 2, the order doesn't matter (playing song A then song B is the same as playing song B then song A).
The formula for combinations is:
C(n, k) = n! / [k!(n-k)!]
where:
- n is the total number of options,
- k is the number of options to choose,
- "!" denotes factorial, which means multiplying all positive integers up to that number.
So in this case, n = 10 (the number of songs they know), and k = 2 (the number of songs in each set list).
C(10, 2) = 10! / [2!(10-2)!] = (10987654321) / [(21)(87654321)] = (109) / (21) = 90 / 2 = 45
So the band could perform 45 different 2-song set lists at their next concert.
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