Q.

Seven girls G1, G2, G3, ..., G7 are such that their ages are in order G1 < G2 < G3 < ….. < G7. Five girls are selected at random and arranged in increasing order of their ages. The probability that G5 and G7 are not consecutive is

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a

2021

b

1921

c

1721

d

1321

answer is C.

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Detailed Solution

Required probability = I - P (G5 and G7 are consecutive)                                 =1− 4C3 7C5=1721
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Seven girls G1, G2, G3, ..., G7 are such that their ages are in order G1 < G2 < G3 < ….. < G7. Five girls are selected at random and arranged in increasing order of their ages. The probability that G5 and G7 are not consecutive is