Arrangement

Probability Level 3

In how many ways can 5 girls and 3 boys stand in a row such that no two boys are together?


The answer is 14400.

Deepak Gowda by Deepak Gowda , 32, India

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1 solution

Deepak Gowda
Jun 6, 2014

possible Arrangement: ---girl---girl---girl---girl---girl---

--- indicates positions available for boys . As there are 3 boys and 6 positions available, arrangement of boys will be 6P3 = 120.

since 5 girls number of arrangement of girls will be 5! = 120

total ways = 5! * 6P3 = 120 * 120 = 14400.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

There is nothing in the question stating that 6 positions are available!

And its a combination problem and not a permutation one!

Abhishek Desai - 7 years ago

It's a question regarding arrangement, so permutation can be applied. In the above solution, he means to say if you place 5 girls spaced out initially, there are 6 vacant positions for the boys to occupy. 4 positions in between the girls and 2 on the extremes.

Siddharth Dias - 6 years, 10 months ago

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