There are total 8 cards, out of them E is twice.
1
If the labels are drawn without replacement :
Probability of drawing G in first = 1/8
Probability of drawing R in second = 1/7
(since in second draw, one label is already taken out)
Probability of drawing E in third = 2/6
(since there are two labels with E character)
Probability of drawing E in fourth = 1/5
(since one label with E is taken out)
Probability of drawing N in fifth = 1/4
Probability of drawing S in sixth = 1/3
Hence probability that labels are drawn in order GREENS
= (1/8)*(1/7)*(2/6)*(1/5)*(1/4)*(1/3)
= 2/20160
= 1/10080
2.
If labels are drawn with replacement :
Probability of drawing G in first = 1/8
Probability of drawing R in second = 1/8
(since before second draw, label with G is kept again )
Probability of drawing E in third = 2/8
(since there are two labels with E character)
Probability of drawing E in fourth = 2/8
(since one label with E is kept again in box before fourth draw)
Probability of drawing N in fifth = 1/8
Probability of drawing S in sixth = 1/8
Hence probability that labels are drawn in order GREENS
= (1/8)*(1/8)*(2/8)*(2/8)*(1/8)*(1/8)
= 4/ 262144
= 1/65536
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