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