Q.3) Suppose that under a revised curriculum, the Hogwarts school admits a total
ID: 2922837 • Letter: Q
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Q.3) Suppose that under a revised curriculum, the Hogwarts school admits a total of 100 US students, 2 from each of the 50 states. Suppose a 8 member student committee is to be formed for general affairs. Find the number of such 8 member committees which have at least one of the two students from New York Further suppose that 50 students show up for Halloween celebration. How many such 50 member groups can be formed with exactly one student from each state? Suppose two different teams each with 10 students- red team and blue team are to be formed for a game of quidditch. Find the number of ways of forming these two teams such that the two New Yorkers are in different teams. (You can consider the two teams to be distinct from each other).Explanation / Answer
a) no. Of student committees with at least one New York student =
no. Of ways in which the other 7 students can be selected = no. Of ways to select 7 out of 99 => 99C7 = 14,887,031,544
b) possible number of 50 such students group => the first student can be either of 2 students from 1st state, second student can also be either of 2 from 2nd state, and so on,
therefore, number of of ways of selecting first student = 2, selecting 2nd student = 2, and so on, (selecting every student is 2)
Therefore total possible groups = 2*2*2*....50 times = 2^50 = 1.1258999*10^15
c) we simply have to find the number of ways to select the other 7 students in both teams = 98C7*91C7
Therefore total teams possible = 2*(98C7)*(91C7) ........(as teams are distinct)
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