A group of four boys (Alex, Bryan, Chris, and David) and five girls (Megan, Nancy, Olivia, Pauline, and Rebecc?

A group of four boys (Alex, Bryan, Chris, and David) and five girls (Megan, Nancy, Olivia, Pauline, and Rebecca) are going to sit together in a row of 9 theater seats.

(a) In how many ways can they seat themselves?

(b) In how many ways can they seat themselves if the boys all sit together and the girls

a) P = 362880 ways

b) P = 2880 ways

Step-by-step explanation:

a) We have four boys and five girls, they are going to sit together in a row of 9 theater seats, without restrictions

We have a permutation of 9 elements

P = 9!

P = 9*8*7*6*5*4*3*2*1

P = 362880 ways

b) Boys must seat together, we have two groups of people

4 boys they can seat in 4! different ways

P₁ = 4!

P₁ = 4*3*2*1

P₁ = 24

And girls can seat in 5! dfferent ways

P₂ = 5!

P₂ = 5*4*3*2*1

P₂ = 120

To get total ways in the above mentioned condition, we have to multiply P₁*P₂

P = 24*120

P = 2880 ways