Question

Problem 7. Find out the number of ways for 8 students and 5 GTAs to stand in a line so that no two GTAs stand next to each other as GTAs standing together may lead to them unnecessarily arguing about who has better teaching skills. Problem 8. Your debit card pin now requires six digits. Solve that: (a) How many possible pins are there. (b) Now the bank requires pins not to reuse digit. How many possible legit pins are there? Problem 9. Without calculation, show that combination (s, a) equals combination (s, (s-a)) using definition, where integers a, s satisfies s > 1, a > 0, s >= a. (should be just one sentence)

          Problem 7. Find out the number of ways for 8 students and 5 GTAs to stand in a line so that no
two GTAs stand next to each other as GTAs standing together may lead to them unnecessarily
arguing about who has better teaching skills.
Problem 8. Your debit card pin now requires six digits. Solve that:
(a) How many possible pins are there.
(b) Now the bank requires pins not to reuse digit. How many possible legit pins are there?
Problem 9. Without calculation, show that combination (s, a) equals combination (s, (s-a)) using
definition, where integers a, s satisfies s > 1, a > 0, s >= a. (should be just one sentence)

Problem 7. Find out the number of ways for 8 students and 5 GTAs to stand in a line so that no
two GTAs stand next to each other as GTAs standing together may lead to them unnecessarily
arguing about who has better teaching skills.
Problem 8. Your debit card pin now requires six digits. Solve that:
(a) How many possible pins are there.
(b) Now the bank requires pins not to reuse digit. How many possible legit pins are there?
Problem 9. Without calculation, show that combination (s, a) equals combination (s, (s-a)) using
definition, where integers a, s satisfies s > 1, a > 0, s >= a. (should be just one sentence)

Added by Sara F.

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