a) The number of k-combinations from a given set S of n elements is C(n, k) = n!/((n - k)! k!)

n = 12, k= 4

C(12, 4) = 12!/((12 - 4)! 4!)

C(12, 4) = 9*10*11*12/(2*3*4)

C(12, 4) = 495 ways

b)12 books are to be arranged on a shelf, however only 10 books can fit on the shelf. How many ways can the 10 books be arranged.

since the odrer of the books is important we have variations

V(n , k) = n!/(n - k)!

in our case n = 12, k = 10

V(12 , 10) = 12!/(12 - 10)

V(12 , 10) = 3*4*5*6*7*8*9*10*11*12

V(12 , 10) = 239,500,800 ways