Question

Enter an inline fraction (a/b) in simplest form. A box contains identical labels that each have one character written on it. All characters together spell GENEROUS. Six labels are drawn, at random, from the box. If the labels are drawn without replacement, the probability that they are drawn in the order that spells GREENS is A and if the labels are drawn with replacement, the probability that they are drawn in the order that spells GREENS is A

Answer 1

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