How many ways are there to put 6 balls in 3 boxes if the balls are distinguishable but the boxes are not? hint(s): the following cases are the most likely to be miscounted: * putting 2 balls into each box. * putting 3 balls into two boxes. * putting 4 balls into a box and 1 ball into the other 2 boxes. the answer is not 207.

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.