a) The arrangement of 9 paintings can be done 9 ways.
b) The arrangement of the 4 out of 9 paintings will be done as 21 ways.
What is the combination?
The arrangement of the different things or numbers in a number of ways is called the combination.
a) Here if she has 9 paintings so the number of the arrangements will be
[tex]^{9} C _2 =\dfrac{9!}{(9-1)!(1!)}\\\\\\^{9} C _2=\dfrac{9!}{8!}\\\\\\^{9} C _2= 9 \ ways[/tex]
b) The arrangement of the 4 out of 9 paintings will be
[tex]^{9}C_{4}=\dfrac{9!}{(9-4)!(4!)}\\\\\\\^{9}C_{4}=21 \ ways[/tex]
Therefore the arrangement of 9 paintings can be done 9 ways and the arrangement of the 4 out of 9 paintings will be done as 21 ways.
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