Homework Sourse3 Suppose that we have a class of 23 girls and 18 boys and w
Solution
In the give problem, total number of children = 23 + 18 = 41
and size of the project team is 10.
a) Possibilities for selecting 10 children from the group of 41 children is given by:
for selecting first children in team no. of possibilities = 41
for selecting second children in the team, no. of possibilities = 40
similarly for selecting tenth children in the team, no. of possibilities = 32
Thus the possibilities for selecting 10 children in order = 41*40*39*38*37*36*35*34*33*32 = 41! / (41-10)!
Also in selecting a team of 10 children the order does not matters so, possibbility of selecting children for team reduces by 10!.
So, the possibility of selecting 10 children out of 41 in a team = 41! / ((41-10)! 10!) = 41C10
Alternatively, by using combination we can directly give the possibilities as 41C10
b) Possibilities for a team to have 4 boys out of total 18 boys and 6 girls out of 23 girls is given by:
For selecting 4 boys out of total 18 boys, possibilities using combination = 18C4
And for selecting 6 girls out of total 23 girls, possibilities using combination = 23C6
Thus possibility of a team having 4 boys and 6 girls = 18C4 * 23C6
c) Possibilities of teams for Graham & Kent in a team is calculated by fixing two seats in the team for them and only 8 children are to be selected from remaining 39 children (41-2). The possibilities of selecting 8 children in remaining 39 children = 39C8
No considering another case when both Graham & Kent are not in the team, so in this case we have to select 10 children out of remainingg 39 children. Possibilities for selcting 10 children out of 39 = 39C10
Thus, for given condition possible teams = 39C8 + 39C10
