Question

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?

Answer 1

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.

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