A store sells 6 dierent colors of shirts with at least 20 of

A store sells 6 dierent colors of shirts with at least 20 of each kind. (a) How many dierent combinations of 20 shirts can be chosen ? (b) If the store has only 9 red shirts but at least 20 of each other colors, how many combinations of 20 shirts can be chosen ? (c) If the store has only 9 red shirts and only 8 blue shirts but at least 20 of each other colors, how many combinations of 20 shirts can be chosen ?

Solution

a) Here 6 dierent colors of shirts with at least 20 of each:6*20=120= 120C₂₀

b) the store has only 9 red shirts but at least 20 of each other colors (100+9)C₂₀=109C₂₀=

c) the store has only 9 red shirts and only 8 blue shirts but at least 20 of each other colors

            (20-9)+(20-8)+(80)C₂₀

                =97C₂₀.