Modern Math

Permutation & Combination

Conceptual

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?

✅ Correct Option: 3

Total ways to select 3 shirts with at least one black shirt

= Total ways to select 3 shirts - Ways to select 3 shirts without any black shirt

Total ways to select 3 shirts = $^9C_3$ = 84

Ways to select 3 shirts without black = $^6C_3$ = 20

(selecting from only white(2) and red(4) shirts)

Therefore, required ways = $^9C_3$ - $^6C_3$

= $84 - 20$

= $64$

Therefore, there are 64 ways of picking out atleast 1 black shirt.

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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?

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