HOTS : Permutations & Combinations

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 x9C13C3 x9C0

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