Prob 2. A colour box has 3 red colours of different shades, 2 white colours of different shades and 7 green colours of different shades. In how many ways can 3 colours be taken from the box if at least one of them is red?
Sol. We have got 3 red colours, 2 white colours and 7 green colours.
There are 3 ways to take 3 colours from the box.
(1) 1red 2 other
(1) 2red 1 other
(1) 3red 0 other
(1) Number of ways to choose 1red = 3C1
Number. of ways to choose 2 others = 9C2
(2) No. of ways to choose 2red = 3C2
No. of ways to choose 1 others = 9C1
(3) No. of ways to choose 3 red = 3C3
No. of ways to choose 0 others = 9C0
Hence the total number of ways is
3C1 x 9C2 + 3C2 x9C1 + 3C3 x9C0