In how many ways 4 girls and 6 boys can be seated in a row so that no two girls are together?
In how many ways 4 girls and 6 boys can be seated in a row so that no two girls are together? the correct answer is 172,800
by J Nandhini
Updated Nov 03, 2023
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In how many ways 4 girls and 6 boys can be seated in a row so that no two girls are together?
The Correct answer is 172,800
First, let's find the total number of ways to arrange the 10 people in a row, which is simply 10!.
Next, let's consider the undesirable case where two or more girls are seated together. We'll treat the group of girls as one entity, which gives us 7 entities in total (1 group of girls and 6 individual boys). This can be arranged in 7! ways. Within the group of girls, there are 4! ways to arrange the girls.
So, the total number of undesirable arrangements is 7! * 4!.
Finally, we can use the principle of complementary counting to find the number of desirable arrangements:
Desirable arrangements = Total arrangements - Undesirable arrangements = 10! - (7! * 4!)
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In how many ways 4 girls and 6 boys can be seated in a row so that no two girls are together? - FAQ
1. In how many ways 4 girls and 6 boys can be seated in a row so that no two girls are together?
172,800
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