Probability help?

3.
a)
Number of combinations of drawing 6 balls without restriction
= C(20,6)
= 20!/(6!14!)
= 38760

When all the 5 blue balls are drawn, one more ball that is not blue must be drawn.
Number of combinations that all the blue balls are drawn
= C(5,5) × C(15,1)
= [5!/(0!5!)] × [15!/(1!14!)]
= 15

P(all the blue balls are drawn on drawing 6 balls)
= 15/38760
= 1/2584


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b)
When all the 3 blue balls and 2 yellow balls are drawn, one more ball that is red or green must be drawn.
Number of combinations that 3 blue balls and 2 yellow balls are drawn
= C(5,3) × C(6,2) × (9,1)
= [5!/(3!2!)] × [6!/(2!4!)] × [9!/(1!8!)]
= 1350

P(3 blue balls and 2 yellow balls are drawn on drawing 6 balls)
= 1350/38760
= 45/1292


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c)
If no green balls are drawn, 6 balls that are not green must be drawn.
Number of combinations that no green balls are drawn
= C(17,6)
= 17!/(6!11!)
= 12376

P(no green balls are drawn on drawing 6 balls)
= 12376/38760
= 91/285


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d)
When no red balls are drawn, 6 balls that are not red must be drawn.
Number of combinations that no red balls are drawn
= C(14,6)
= 3003

When 1 red ball is drawn, 5 more balls that are not red must be drawn.
Number of combinations that 1 red ball is drawn
= C(6,1) × C(14,5)
= [6!/(1!5!)] × [14!/(5!9!)]
= 12012

Number of combinations that at least 2 red balls are drawn
= 38760 - 3003 - 12012
= 23745

P(At least 2 balls are drawn on drawing 6 balls)
= 23745/38760
= 1583/2584