Anna and Mark

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imago: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Sun Sep 09, 2007 3:34 am; Location: spain

by imago » Tue Sep 18, 2007 1:27 pm

Anna and Mark are included in a group of 8 people. If 4 people are selected at random and without replacement from this group, what is the probability that Mark and not Anna will be selected?

a.1/7
b.2/7
c.3/7
d.4/7
e.5/7

OA: b

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Source: Beat The GMAT — Problem Solving | Tue Sep 18, 2007 1:27 pm

kajcha: Master | Next Rank: 500 Posts; Posts: 321; Joined: Tue Aug 28, 2007 5:42 am; Thanked: 1 times

by kajcha » Tue Sep 18, 2007 2:01 pm

It is B

Suppose the combination of people selected is Mxxx

where x represents any person other than Anna

Probability of this combination = (1/8)*(6/7)*(5/6)*(4/5) = 1/14

Now Mark can be selected at 2nd, 3rd or 4th position too. so,

total probability = 4*1/14 = 2/7

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