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Sagot :
Given:
Number of boys = 5
Number of girls = 4
To find:
The number of ways in which 5 boys and 4 girls be arranged on a bench if there are no restrictions.
Solution:
We have, 5 boys and 4 girls.
Total number of boys and girls:
[tex]5+4=9[/tex]
If there are no restrictions, then the total number of ways to arrange 9 persons is:
[tex]^9P_9=\dfrac{9!}{(9-9)!}[/tex]
[tex]^9P_9=\dfrac{9!}{0!}[/tex]
[tex]^9P_9=\dfrac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{1}[/tex]
[tex]^9P_9=362880[/tex]
Therefore, the total number of ways to arrange 5 boys and 4 girls is 9! or 362880.
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