Question

Six country music bands and 3 rock bands are signed up to perform at an all-day festival. How many different orders can the bands play in if
A.there are no restrictions on the order?
B. all the bands of each type must perform in a row?

Answer 1

Answer:

a. 9 orders of play b. 9 orders of play

Step-by-step explanation:

a. There are 6 country music bands and 3 rock music bands. Since, there are no restrictions on the order of play, we use combination theorem. So Combination, ⁿCₓ = $\frac{n!}{x!(n-x)!}$ . The total number of bands n = 6 + 3 = 9. x = 1 , because we combine it in one way, since only one band can perform at a time.  ⁹C₁ = $\frac{9!}{1!(9-1)!}$=9!/8!= 9 orders of play.

b. Since all the bands of each type must perform in a row, we use permutation theory. ⁿPₓ where n = number of bands and x = number of ways to be permuted. For the country music bands, n = 6 and x =1 (since only one band can perform at a time). ⁶P₁ = 6 orders of play. For the rock bands, n = 3 and x =1 (since only one band can perform at a time). So, ³P₁ = 3 orders of play. The total different number of orders is ⁶P₁ + ³P₁ = 6 + 3 = 9 orders of play.