Question

How many ways are there to seat six boys and seven girls in a row of chairs so that none of the girls sit together. A detailed explanation would be most appreciated.

Answer 1

5040 ways

Explanation:

There will be 13 chairs altogether.

Since there are 7 girls who cannot sit together, the pattern will be alternate.

→ G, B, G, B, G, B, G, B, G, B, G, B, G

• Means the ways of girls seated = 7!
• No. of ways of boys seated = 6!

Total Ways

• 7! x 6!
• 6! (7 x 1)
• 6 x 5 x 4 x 3 x 2 x 1 x 7
• 720 x 7
• 5040 ways