The question is an illustration of permutation and combinations.
- The number of ways she can choose 4 out of the 7 paintings is 35
- The number of ways she can arrange 4 out of the 7 paintings is 840
The given parameters are:
<u>(a) Choose 4 of 7 paintings</u>
Choosing 4 of 7 paintings implies combination.
So, we have:
Substitute values for n and r
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Hence, the number of ways she can choose 4 out of the 7 paintings is 35
<u>(b) Arrange 4 of 7 paintings</u>
Arranging 4 of 7 paintings implies permutation.
So, we have:
Substitute values for n and r
Expand
Hence, the number of ways she can arrange 4 out of the 7 paintings is 840
Read more about permutation and combinations at:
brainly.com/question/15301090