40,320
Harvard has several rooming arrangements availableÊfor students. Students can live in gender neutral housing or in married and family housing.
Factorial 8, ie 8 x 7 x 6 x 5 x 4 x 3 x 2 = 40320
Apex: Permutations
There are no special health and safety arrangements for school rooms in which students take examinations.
To arrange the 3 girls into the first 3 places:The first place can be any one of 3 girls.The second place can be either of the remaining 2 girls.The number of different possible arrangements of the first 3 places is (3 x 2) = 6In a similar way, we can show that the number of different ways to line up the 7 boys is(7 x 6 x 5 x 4 x 3 x 2) = 5,040 .So the total number of arrangements of all 10 students is (6 x 5,040) = 30,240
There are 10560 possible committees.
24
TARC AFA students?
TARC AFA students?
There are 10 different sets of teachers which can be combined with 4 different sets of students, so 40 possible committees.
There are (10 x 9)/2 = 45 different possible pairs of 2 teachers. For each of these . . .There are (30 x 29)/2 = 435 different possible pairs of students.The total number of different committees that can be formed is (45 x 435) = 19,575 .
To determine the number of different committees that can be formed from 11 teachers and 48 students, we need to clarify the size of the committee and whether there are any restrictions on the selection. If we assume that any combination of teachers and students can be chosen without restrictions, the total number of possible combinations is (2^{11} \cdot 2^{48} = 2^{59}). This accounts for every possible subset of teachers and students, including the empty committee.