Question

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Answer 1

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

$^{9} C _2 =\dfrac{9!}{(9-1)!(1!)}\\\\\\^{9} C _2=\dfrac{9!}{8!}\\\\\\^{9} C _2= 9 \ ways$

b) The arrangement of the 4 out of 9 paintings will be

$^{9}C_{4}=\dfrac{9!}{(9-4)!(4!)}\\\\\\\^{9}C_{4}=21 \ ways$

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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