Answer:
b = (T - a - c - d) / 3
Step-by-step explanation:
Let T be the total number of points required to advance.
a, c and d are points scored in the local matches, and b is the number of points scored in the district match. If b is worth 3 times as much as the other matches, the total number of points is given by:
Isolate b in order to find out how many points they need in the district match:
They need to score (T - a - c - d)/3, in the district match in order to win.
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