How many Bit strings of length 10 contain:

a) exactly four 1's
10!/4!6! = 10*9*8*7/4*3*2*1 = 3*3*4*7 = 210

b) at most four 1's
10!/4!6! + 10!/3!7! + 10!/2!8! + 10!/9!1! = 210 + 120 + 45 + 10 = 385

c) at least 4 1's
I found this by finding the answer for at most 6 0's
252 + 210 + 120 + 45 + 10 = 847

d) equal number of 1's and 0's
10!/5!5! = 252