Question
Match each item given under the column C1 to its correct answer given under the column C2.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
C1
C2
(a)
Boys and girls alternate.
(i)
5! × 6!
(b)
No two girls sit together.
(ii)
10! – 5! 6!
(c)
All the girls sit together.
(iii)
(5!)2 + (5!)2
(d)
All the girls are never together.
(iv)
2! 5! 5!

Answer

C1
C2
(a)
Boys and girls alternate.
(iii)
(5!)2 + (5!)2
(b)
No two girls sit together.
(i)
5! × 6!
(c)
All the girls sit together.
(iv)
2! 5! 5!
(d) All the girls are never together. (ii) 10! – 5! 6!
Explanation:
Total number of arrangment when boys and girls alternate: = (5!)2 + (5!)2
  1. No two girls sit together: = 5! 6!
  2. All the girls sit never toghether = 2! 5! 5!
  3. All the girls sit never together = 10! - 5! 6!

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