The following questions may be answered with an integer (e.g., "0") or combination/permutation notation (e.g., "C(1,1)") or factorial notation (e.g., "1!") or "Yes"/"No". Please use + and * for addition and multiplication.

10 student helpers have appeared on campus to help set up for Open Day. Of these, 4 are Engineering students and 6 are IT students.

a) If 5 student helpers are needed to help move a large table, how many different arrangements of students are there for this task?

b) Following on from a), what if this group needed to contain exactly 3 Engineering students and 2 IT students?

c) There are 3 different locations that need 1 of these student helpers. How many ways could this be arranged?

d) If all 10 student helpers line up for their lunch voucher, how many ways could this queue be formed?

e) Amongst those 10 student helpers, is it guaranteed that two students were born in the same month?