Please show work How many 8member committees can be formed f

Please show work

How many 8-member committees can be formed from a class consisting of 25 students? What if two particular students must be included on the committee? In a game of musical chairs, 11 children will sit in 8 chairs arranged in a row. Three children will be left out. In how many ways can the 11 children find seats?

Solution

Total number of students are 25. We need a committe with meber of 8, it can be possible in 25 C 8 ways .

25 C 8 = 25! / (25-8)! * 8! = 1081575 ways

Now, we want to include set of 2 people in must it can be possible with 23 C 6 * 2 C 2 ways

23 C 6 * 2 C 2 = 23! / (23-6)! * 6! * 1 = 100947 ways