‘Sam and the Matheletes Band’ can play eight Dad-Rock songs, six Show Tunes and four Electro-
Pop songs. In how many ways can Sam’s band choose three pieces to play if Mr. Kassil wants to hear
at least 2 of either Dad-Rock and/or Electro-Pop? (Example selections: all Electro-Pop, all Dad-
Rock, 1 of each etc...)
3 years ago
D: Dad-Rock E: Electro-Pop S: Show-Tunes
It is easier we first calculate the complementary event:
A: At least 2 D and/or E
A': At least 2 S
We have two scenarios for A':
1) 3S: n1=6C3=20
2) 2S and 1D/E: n2=(6C2)*(12C1)=180
n(A')=n1+n2=20+180=200
The total number of selections without any restriction is:
n(U)=18C3=816
Then:
n(A)=n(U)-n(A')=816-200=616
3 years ago
Answered By Majid B
D: Dad-Rock E: Electro-Pop S: Show-Tunes
It is easier we first calculate the complementary event:
A: At least 2 D and/or E
A': At least 2 S
We have two scenarios for A':
1) 3S: n1=6C3=20
2) 2S and 1D/E: n2=(6C2)*(12C1)=180
n(A')=n1+n2=20+180=200
The total number of selections without any restriction is:
n(U)=18C3=816
Then:
n(A)=n(U)-n(A')=816-200=616