A Phys. teacher is training his class for track and field try outs. There are seven event leaders and forty-two students.

A Phys. Ed. teacher is training his class for track and field try outs. There are seven event leaders and forty-two students. The first event is running long jump, and requires two event leaders and twenty- five students. The second event is the 100 m dash, and requires two event leaders and ten students. The third event is the high jump, and requires three event leaders and seven students.

a.    How many ways can the event leaders be chosen for the high jump?

b.    How many ways can students be chosen for the 100 m dash?

c.    In how many ways can the students be arranged if Sarah and Nicki both need to be at the first event, and Todd and Mike need to be in the high jump?