A rock group needs to choose 3 songs to play at the annual Battle of the Bands. How many ways can they choose their set if have 15 songs to pick from?

Expert Solution

A rock group has to choose 3 songs out of 15 songs to play at the annual battle of the bands.

The number of ways in which the rock group can pick 3 songs from 15 songs will be equal to the number of combinations of 15 objects taking 3 at a time.

Use the general formula of combinations,

C(n, r) = n!/r!(n – r)! ...... (1)

Substitute n = 15 and r = 3 in (1) and simplify,

C(15, 3) = 15!/3!(15 – 3)!

= (15 × 14 × 13 × 12!)/(3 × 2 × 1) × 12!

= 455

Therefore, the rock group can pick 3 songs from 15 songs in 455 ways.

Junaid answered 1 year ago

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