1 answer:
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A.
If we take 7 paintings to be hung in 7 spaces side by side, the first space can have any one of the 7 paintings, the second space can have any one of the remaining 6 paintings (as 1 is already hung), the third space can have any one of the remaining 5 paintings (as 2 already hung)...It goes on like this.
So we have ways to arrange all the paintings from left to write. <em>(in factorial notation it is 7!=5040)</em>
B.
We use combinations rather than permutations because order doesn't matter. If we name the paintings A,B,C,D,E,F, and G, groups of 3 paintings of ABC or ACB are the same. So we evaluate using the combination formula,
We have,
C.
This is similar to part A in some ways. Any 3 pictures can be arranged in different ways.
. So, 6 different ways.
ANSWER:
A) 5040 ways
B) 35 different groups
C) 6 ways