There are 95 girls and 87 boys in year 13 at a school. one girl is going to be chosen for the role of head girl. a different girl is going to be chosen for the role of deputy head girl. one boy is going to be chosen for the role of head boy. a different boy is going to be chosen for the rule of deputy head boy. work out how many different ways this can be done.

For the first role, you have 95 girls then to those are 95 possibilites for the role of Head Girl.

For the second role, you are left with 94 girls, the you have 94 possibilities for the role of Deputy Head Girl.

So far, you have 95*94 different ways to conform the group.

Yet you have to combine thosw with the ways to choose the boys.

That is 87 boys for Head Boy and 86 boys for Deputy Head Boy => 87*86 diferent ways.

Finally, the total number of different groups that can be conformed is:

95*94*87*86 =   69,657,420

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