Question

Thirteen people on a softball team show up for a game. (a) How many ways are there to choose 10 players to be in the game? (b) How many ways are there to assign 10 people out of the 13 to the various positions on the field? (c) Of the 13 people, three are college students. How many ways are there to choose 10 players to take the field if at least one of these players must be a college student?

Answer 1

Given there are are 13 people on a softball team thon up for a game. Ea) here we have to choose 10 people from apply combination formula, że. There are Beso ways to choose to is people. So we should playeds. 3 C10 18! *ket ! = "*12*12 286 ways to choose 10 players in the game. (b) there we have to assign 10 people and of the il to the various position, so for ud position we have 13 choices. for and posetion we have 12 choices. for god position we have in chorces. for noth posiberon ve idare a choices. hence total number of ways to assign 10 people = 13812811810892882262584. (c) of the 13 people, there are college students we have to find number of ways to choose 10 players to have the field of at least one of the players must be a college student. Clearly dhon as cosplesent of the "thede is no college student in the players team". fie, we have 10 people for 10 players which doesn't include college student. ... There is only one way to choose 10 players which doesn't . include college slendent. Hence required answer is numbe of ways to choose 10 players - 1 = 286-1 = 285, hence these are 285 ways to choose to players such that at least one of the must be a college student.