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  • 6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is A. 1/432 B. 12/431 C. 1/132 D. none of these

6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is
A. 1/432
B. 12/431
C. 1/132
D. none of these

Answers (1)

Let us consider group 1 where all girls sit together,

Thus,

G

G

G

G

G

G

6 BOYS

Total persons = 1 + 6

                        = 7

Now, total no. of arrangements in row of 7 = 7!

Also, the ways in which girls interchange their seats is 6!

Probability = no. of favorable outcomes/ total no. of outcomes

                        = 6! 7! / 12!

                        = 6 x 5 x 4 x 3 x 2 x 1 x 7! / 12 x 11 x 10 x 9 x 8 x 7!

                        = 6 x 5 x 4 x 3 x 2 / 12 x 11 x 10 x 9 x 8  

                  = 1 / 2 x 11 x 2 x 3 x 2

                  = 1 / 132

Thus, option C is the correct answer.

Posted by

infoexpert22

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