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Question 12 : A box contains 2 white shirts, 3 black shirts, and 4 red shirts. In how many ways can 3 shirts be drawn from the box, if at least one black shirt is to be included in the draw?
Two White Shirts - W1, W2
3 Black Shirts - B1, B2, B3
4 red Shirts - R1, R2, R3, R4
At least 1 black shirts - We cannot have 0 black shirts
When 1 Black Shirt is selected.
|1 (3 ways)||0 (1 way)||2 (4C2) = 6 ways||3 × 1 × 6 = 18 ways|
|1 (3 ways)||2 (1 way)||0||3 × 1 = 3 ways|
|1 (3 ways)||1 (2 ways)||1(4 ways)||3 × 2 × 4 = 24 ways|
|2 (3C2) = 3 ways||1 (2C1) = 2 ways||0||3 × 2 = 6 ways|
|2 (3C2) = 3 ways||0||1 (4C1) = 4 ways||3 × 4 = 12 ways|
|3 (3C3) = 1 way||0||0||1 way|
The question is " A box contains 2 white shirts, 3 black shirts, and 4 red shirts. In how many ways can 3 shirts be drawn from the box, if at least one black shirt is to be included in the draw? "
Choice C is the correct answer.
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