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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?

Oct 31, 2017

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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

Oct 31, 2017
edited by CPhill  Oct 31, 2017
edited by CPhill  Nov 1, 2017