Question

15 people on a softball team show up for a game. ch 06 sec 3 ex 28 (a) - combinations & permutations how many ways are there to choose 10 players to take the field?

Answer 1

There are 3003 ways to choose 10 players from a team of 15.

Step-by-step explanation:

To choose 10 players to take the field from a team of 15 people, we need to find the number of combinations. In this case, the order in which the players are chosen does not matter, so we can use combinations instead of permutations. The formula for combinations is C(n, r) = n! / (r! * (n-r)!), where n is the total number of people and r is the number of players needed.

Plugging in the values, we have C(15, 10) = 15! / (10! * (15-10)!) = 3003. Therefore, there are 3003 ways to choose 10 players to take the field from a team of 15 people.

Answer 2

There are 3003 different ways to choose 10 players out of a team of 15 to take the field in a softball game, calculated using the formula for combinations.

Step-by-step explanation:

To determine how many ways there are to choose 10 players to take the field from a team of 15, we need to calculate the number of combinations. Combinations can be found using the formula for combinations, which is C(n, k) = n! / [k!(n - k)!], where n is the total number of items, and k is the number of items to choose.

Applying this to the current problem:

1. The total number of players (n) = 15.
2. The number of players to choose (k) = 10.
3. Therefore, C(15, 10) = 15! / [10!(15 - 10)!]
4. This simplifies to C(15, 10) = 15! / (10!5!)
5. Calculate: C(15, 10) = (15×14×13×12×11) / (5×4×3×2×1)
6. C(15, 10) = 3003

So, there are 3003 different ways to choose 10 players out of 15 to take the field in a softball game.