In how many ways can a team of 5 players and a coach be chosen from 10 players and 5 coaches? How many of these teams will contain Alex, one of the player?
10P5*5=1260
1260*5/10=630
so 1260 possible teams, half will contain alex
Same person i know the answer to the first part is 1260. I don't know how many teams will have Alex.
To solve this problem, we can use the concept of combinations.
First, let's calculate the total number of ways to choose a team of 5 players and a coach from the given pool of 10 players and 5 coaches.
The number of ways to choose 5 players from 10 can be found using the combination formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of players and r is the number of players to be chosen. So, C(10, 5) will give us the number of ways to choose 5 players from 10, which is 252.
Similarly, the number of ways to choose 1 coach from 5 can be calculated using C(5, 1), which is 5.
Now, we need to find how many of these teams will contain Alex, one of the players.
If Alex is chosen, we can select the remaining 4 players from the remaining 9 players (excluding Alex). So, the number of ways to choose the remaining 4 players is C(9, 4), which is 126.
To calculate the total number of teams that contain Alex, we multiply the number of ways to choose Alex (1) with the number of ways to choose the remaining 4 players (126). So, we have 1 * 126 = 126 teams.
Therefore, the total number of ways to choose a team of 5 players and a coach from 10 players and 5 coaches is 252, and out of these, 126 teams will contain Alex.