Alicia has 7 paintings she wants to hang side by side on her wall.
In how many ways can she arrange all 7 paintings?
If she only wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display?
In how many ways can she arrange 4 out of the 7 paintings?
The table shows the number of touchdowns Luis scored during his football games.
Create a probability distribution table.
What is the probability of Luis scoring 2 touchdowns?
What is the probability of Luis scoring more than 1 touchdown?
What is the estimated value of the number of touchdowns Luis scores?
+130020 Total possible arrangements = 7! = 5040
Total ways to choose 4 of the paintings = C(7,4) = 35 ways
Total arrangements of any 4 = 4! = 24 ways
Probability of Luis scoring 2 touchdowns = [ 7 ] / [ 6 + 10 + 7 + 5 ] = 7/28 = 1 / 4
Probability of Luis scoring more than 1 touchdown = [ 7 + 5 ] / 28 = 12/28 = 3 / 7
Estimated value = weighted average =
[ 6*0 + 10*1 + 7*2 + 5*3 ] / 28 \
[ 10 + 14 + 15 ] / 28 =
[ 39 ] / [28 ] ≈ 1.4 touchdowns
