there is 2 freshmen, 4 sophomores, 8 juniors, and 15 seniors. A local television station wants to interview 8 students from the team. How many different ways can exactly 4 seniors and 4 juniors be selected for the interview?
To find the number of different ways to select exactly 4 seniors and 4 juniors for the interview, we can use the concept of combinations.
Step 1: Determine the number of ways to select 4 seniors from 15 seniors.
This can be calculated using the combination formula: nCr = n! / (r!(n-r)!)
So, the number of ways to select 4 seniors from 15 can be calculated as 15C4 = 15! / (4!(15-4)!) = (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1) = 1365.
Step 2: Determine the number of ways to select 4 juniors from 8 juniors.
Similar to step 1, the number of ways to select 4 juniors from 8 can be calculated as 8C4 = 8! / (4!(8-4)!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70.
Step 3: Multiply the results from step 1 and step 2 to find the overall number of ways to select 4 seniors and 4 juniors for the interview.
Total number of ways = 1365 * 70 = 95,550.
Therefore, there are 95,550 different ways to select exactly 4 seniors and 4 juniors for the interview.