Exercise 143 Page 644

Practice makes perfect

a Since each position has its own special responsibility, the order of selection matters. This means we must use a permutation to find the number of arrangements. The roster is 16 players and we need to select 6 of them. With this information we can write the following equation.

_(16)P_6 =16!/( 16- 6)! ⇔ _(16)P_6 =16!/10! Let's determine this on our graphing calculator.

Akio can form his starting team in 5 765 760 ways.

b If Sidney is already selected for the libero position then there are 15 players left in the team and 5 remaining positions to fill. Therefore, we have to determine _(15)P_5.

_(15)P_5 =15!/( 15- 5)! ⇔ _(15)P_6 =15!/10! Let's determine this on our graphing calculator.

There are 360 360 teams where Sidney plays in the libero position.

c From Part A we know that there are a total of 5 765 760 starting team possibilities. In Part B, we calculated that in 360 360 teams Sidney is drafted for the libero position. With this information we can calculate the probability of Sidney getting chosen as the starting libero.

P(Sidney as libero)=360 360/5 765 760=6.25 %

d If Akio chooses six players without regard to who plays which position then the order of selection does not matter. In this case, we have to calculate the number of combinations that Akio can put together. In other words, we want to determine _(16)C_6.

_(16)C_6=_(16)P_6/6! ⇔ _(16)C_6=16!/10! 6! Let's calculate this using a graphing calculator.

There are 8008 teams that Akio can select without regard to who plays what position. If Sidney is chosen, there are 15 players left and 5 positions. Therefore, by determining _(15)C_5 we can determine how many teams include Sidney

In 3003 teams, Sidney is one of the players. With this information, we can calculate the probability of Sidney getting chosen as one of the players. P(Sidney chosen)=3003/8008=37.5 %