Permutation and Combination Question

Question

A bookshelf displays different types of books, 6 books in English (E) and 5 books in Spanish (S). If 4 books are chosen among the English language books and 3 are selected from the Spanish language books, calculate how many ways can the 7 books be arranged on a shelf given that

i) There are no restrictions (no concern on the sequence)?

ii) 4 English books must put together?

iii) English and Spanish books must put alternately (i.e. ESESESE).

I am confused. Do I need to apply the combinations method first in order to select the books? or I can just directly solve this problem by using permutation? Please help me solve these questions :(

Answer 1

1] (6 choose 4)*(5 choose 3) * 7!

2] (6 choose 4)*(5 choose 3) * 4

EEEESSS

SEEEESS

SSEEEES

SSSEEEE

3] (6 choose 4) * (5 choose 3) * 3! * 4!

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(6 choose 4) = 6!/( 4! 2!) = 6*5/2 = 15

(5 choose 3) = 5!/(3!2!) = 5*4/2 = 10

you can now use your calculator to finish them off