The total number of ways a girl can choose a two-piece outfit from 9 blouses and 8 skirts is 72.
Permutation is a mathematical calculation of the number of ways a particular set can be arranged, where order of the arrangement matters.
[tex]^{n} P_{r} = \frac{P!}{(n-r)!}[/tex]
Where,
[tex]^{n}P_{r}[/tex] is permutation
n is the number of objects
r is the number of objects selected.
According to the given question.
Total number of blouses = 9
Total number of skirts = 8
So,
the number of ways of choosing one blouse from 8
=[tex]^{8} P_{1}[/tex]
= [tex]\frac{8!}{(8-1)!} \\[/tex]
= [tex]\frac{8!}{7!}[/tex]
= [tex]\frac{8\times 7!}{7!}[/tex]
= [tex]8[/tex]
And the number of ways of choosing one skirt from 9
[tex]^{9} P_{1} \\= \frac{9!}{(9-1)!} \\= \frac{9\times 8!}{8!} \\=9[/tex]
Therefore,
The total number of ways of choosing two piece outfit from 9 blouses and 8 skirts
= [tex]^{8} P_{1} \times ^{9} P_{1}[/tex]
= [tex]8 \times 9[/tex]
[tex]= 72[/tex]
Hence, the total number of ways a girl can choose a two-piece outfit from 9 blouses and 8 skirts is 72.
Find out more information about permutation here:
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