a jar contains 5 black buttons and seven brown buttons. If 6 buttons are picked at random what is the probability that exactly two of them are black

Answer 1

the denominator is (12 choose 6) = 12*11*10*9*8*7 / 6*5*4*3*2 =

11 *10*9*8*7/ 5*4*3 <--- 12 cancels 6*2

11 * 2 * 9 *8*7 / 4*3 <--- 10 cancels 5

11 *2 * 3 * 2 * 7 / <--- 9 cancels 3 and 8 cancels 4

924

the numerator is (5 choose 2) * (7 choose 4) = 350

the probability is 350/924 = 175/462

factors of 175 are 5 and 7 neither of which divides 462

the probability is 175/462 = 37.87% = 37 and 29/33 %