Symbiosis National Aptitude Test SNAP 2013 Paper

Question : 20 of 150

Marks: +1, -0

There are five boys and three girls who are sitting together to discuss a management problem at a round table. In how many ways can they sit around the table so that no two girls are together?

1220
1400
1420
1440

Validate

Solution:

We have no girls together, let us first arrange the 5 boys and after that we can arrange the girls in the space between the boys.
Number of ways of arranging the boys around a circle = [5 – 1]! = 24.
Number of ways of arranging the girls would be by placing them in the 5 spaces that are formed between the boys. This can be done in

\,↖{5}P_3

ways = 60 ways.
Total arrangements = 24 × 60 = 1440.

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