66. Professor Grinch's telephone number is 6328363. Mickey remembers the collection of digits but not their order, except that he knows the first 6 is before the first 3. How many arrangements of these digits with this constraint are there? Student Guide Solution: 7 x 6 x 4 Be sure to explain your solution. 70. How many ways are there to pick a group of n people from 100 people (each of a different height) and then pick a second group of m other people such that all people in the first group are taller than the people in the second group? Student Guide Solution: C(100, m + n) Be sure to explain your solution. 4. How many ways are there to invite one of four different friends over for dinner on five successive nights such that no friend is invited more than three times? Student Guide Solution: 45 - 4 x 5!/1!4! - 5(5!/5!) Be sure to explain your solution.8. Ten different people walk into a delicatessen to buy a sandwich. Four always order tuna sh, two always order chicken, two always order roast beef, and two order any of the three types of sandwich. (a) How many different (unordered) collections of sandwiches are possible? (b) How many different sequences of sandwiches are possible? Student Guide Solution: a) C(2+31,2) b) 10![1/6!2!2! + 2/4142! + 2/5232: + 1/423:3!] Be sure to explain your solution. 12. How many ways are there to pick nine balls from large piles of (identical) red, white, and blue balls plus one pink ball, one lavender ball, and one tan ball? Student Guide Solution: 2k C(3, k) x C((9 - k) + 3 - 1, (9 - k)) Be sure to explain your solution. 22. How many arrangements of the letters in PEPPERMILL are there with (a) The M appearing to the left of all the vowels? (b) The rst P appearing before the rst L? Student Guide Solution: a) 3 x 10!/4!3!2!1! b) NOT ANSWERED Be sure to explain your solution