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# probability

there are 6 students(A-F)standing in a row,find the probability that any two of A,B and C do not stand next to each other.

4 girls and 8 boys are arranged in a row at random. Find the probability that any 2 girls do not stand next to each other.

### 1 Answer

- fooksLv 77 years agoFavorite Answer
There are 6 students(A-F)standing in a row, find the probability thatany two of A,B and C do not stand next to each other.

Solution :

If the 6 students stand in a row without restriction :

Number of ways = 6P6

If any two of A, B and C do not stand next to each other :

Firstly, arrange D, E and F (denoted as X) in a row (3P3): _X_X_X_

Then, Put A, B and C in any three spaces "_" (4P3).

Number of ways = 3P3 x 4P3

The required probability

= 3P3 x 4P3 / 6P6

= 3! x (4!/1!) / 6!

= 1/5

4 girls and 8 boys are arranged in a row at random.Find the probability that any 2 girls do not stand next to each other.

Solution :

If the 12 persons (4 girls and 8 boys) are arranged in a row withoutrestriction :

Number of ways = 12P12

If any 2 girls do not stand next to each other :

Firstly, arranged the 8 boys (B) in a row (8P8) :_B_B_B_B_B_B_B_B_

Then, Put the 4 girls in any 4 spaces "_" (9P4).

Number of ways = 8P8 x 9P4

The required probability

= 8P8 x 9P4 / 12P12

= 8! x (9!/5!) / 12!

= 14/55

Source(s): fooks- Login to reply the answers