*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 = ^{3}C_{1}

Number. of ways to choose 2 others = ^{9}C_{2}

(2) No. of ways to choose 2red = ^{3}C_{2}

No. of ways to choose 1 others = ^{9}C_{1}

(3) No. of ways to choose 3 red = ^{3}C_{3}

No. of ways to choose 0 others = ^{9}C_{0}

Hence the total number of ways is

^{3}C_{1} x ^{9}C_{2} + ^{3}C_{2} x^{9}C_{1} + ^{3}C_{3} x^{9}C_{0 }