There are ten seniors and five juniors in the Math Club at Jefferson High School. In how many ways can a math team consisting of four seniors and three juniors be selected from members of the Math Club?
Well, selecting the members of the math team is like picking out an outfit for a fancy party. You have 10 seniors to choose from for the first spot on the team, then 9 seniors left for the second spot, and so on until you've filled all 4 senior spots.
So, the number of ways to select the seniors would be 10 * 9 * 8 * 7.
Similarly, for the juniors, you have 5 juniors to choose from for the first spot, then 4 juniors left for the second spot, and so on until you've filled all 3 junior spots.
So, the number of ways to select the juniors would be 5 * 4 * 3.
Now, just multiply the number of ways to select the seniors by the number of ways to select the juniors to get the total number of ways to form the math team:
(10 * 9 * 8 * 7) * (5 * 4 * 3) = 30240.
So, there would be 30,240 different ways to select a math team consisting of 4 seniors and 3 juniors from the Math Club. Time to do some math-fun!
To calculate the number of ways a math team consisting of four seniors and three juniors can be selected from the Math Club, we will use a combination:
The number of ways to choose four seniors out of ten is given by the combination formula: C(10, 4) = 10! / (4! * (10-4)!) = 210.
Similarly, the number of ways to choose three juniors out of five is: C(5, 3) = 5! / (3! * (5-3)!) = 10.
To find the total number of ways to select the math team, we will multiply these two combinations:
Total ways = C(10, 4) * C(5, 3) = 210 * 10 = 2100.
Therefore, there are 2100 different ways to select a math team consisting of four seniors and three juniors from the Math Club at Jefferson High School.
To find the number of ways to select a math team consisting of four seniors and three juniors from the Math Club, you can use the concept of combinations.
The number of ways to choose four seniors from a group of ten seniors is given by the combination formula: C(n, r) = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items to be chosen.
In this case, n = 10 (number of seniors) and r = 4 (number of seniors to be chosen). Substitute these values into the formula:
C(10, 4) = 10! / (4! * (10 - 4)!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210.
Therefore, there are 210 ways to select four seniors from the group of ten seniors.
Similarly, the number of ways to choose three juniors from a group of five juniors is:
C(5, 3) = 5! / (3! * (5 - 3)!) = 5! / (3! * 2!) = (5 * 4) / (2 * 1) = 10.
Therefore, there are 10 ways to select three juniors from the group of five juniors.
To determine the total number of ways to choose a math team consisting of four seniors and three juniors, multiply the number of ways to choose the seniors by the number of ways to choose the juniors:
210 * 10 = 2100.
Hence, there are 2100 ways to select a math team consisting of four seniors and three juniors from the Math Club at Jefferson High School.
choose the seniors in C(10,4) ways
choose the juniors in C(5,3) ways.
Multiply those