Probability help!!! With steps please
Statistics

Tutor: None Selected  Time limit: 1 Day 
A Jar has 20 marbles in it, 5 of which are yellow, the rest green. You are selecting 6 at a time. What is the probability that:
you get exactly 1 yellow? Probability at least 2 are yellow?
This is a binomial distribution with P(S) = 5/20 =1/4 of choosing a yellow marble.
Six out of 20 are chosen so number of combinations
= (20 x 19 x 18 x 17 x 16 x 15) x 1/ 6!
=3870
More time needed will take another 20 mins
P(first marble is yellow, remaining 5 are green) = 5/20 x P( choosing sequence of 5 green out of 19 without replacement)
= 1/4 x 15/19 x 14/18 x 13/17 x 12/16 x 11/15
= 360360/1395360
But yellow could come in 6 different ways
P(one yellow) = 1001/6460
Second part  doing
P(0 yellow) = P(sequence of 6 greens from 20 without replacement)
= 15/20 x 14/19 x 13/18 x 12/17 x 11/16 x 10/15
=3603600/27907200
=1001/7752
Hence P(of 0 or 1 yellow) = 1001/66460 + 1001/7752
= 11011/38760
Hence P( at least 2 yellow) = 1  P(0 or 1 yellow)
=1 11011/38760
= 27749/38760
Number of ways of choosing any 6 from 20 = 20 C 6 = Six out of 20 are chosen so number of combinations
= (20 x 19 x 18 x 17 x 16 x 15) x 1/ 6!
=38760
Number containing 5 greens and 1 yellow from these =
Number of ways of choosing 5 greens from 15 and 1 yellow from 5 yellows
= 15 C5 x 5
= (15 x 14 x 13 x12 x 11/ 5!) x 5
= 15015
Hence P(one yellow) = 15015/38760 = 1001/2584
Final please ignore all others
Part 1
Number of ways of choosing any 6 from 20 = 20 C 6 = Six out of 20 are chosen so number of combinations
= (20 x 19 x 18 x 17 x 16 x 15) x 1/ 6!
=38760
Number containing 5 greens and 1 yellow from these =
Number of ways of choosing 5 greens from 15 and 1 yellow from 5 yellows
= 15 C5 x 5
= (15 x 14 x 13 x12 x 11/ 5!) x 5
= 15015
Hence P(one yellow) = 15015/38760 = 1001/2584
Part 2
Second part
Number containing 0 yellows = 15 C 6 = 15 x 14 x 13 x 12 x 11 x 10 x 1/6! = 5005
Hence P( 0 yellows) = 5005/38760 = 1001/7752
Hence P(at least 2 yellows) = 1 1001/2584 – 1001/ 7752
1 4004/7752
= 3748/7752
= 937/ 1938
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