Question

6. A box contains 8 novels and 7 math books going to loan 6 books to a friend. How many different (a) You are book selections could your friend receive? going to loan 3 novels and 4 math books to a friend. How (b) You are many different book selections could your friend receive? (c) You are going to loan at least 13 books to a friend. How many different book selections could your friend receive? going to loan at least 3 books to a friend. How many (d) You are different book selections could your friend receive? (e) You wish to display 8 books on the shelf. You want 4 of them to be math books and 4 novels. In how many ways can this be done? 7. There are 10 children, and 4 identical toys to distribute among them. In how many ways can this be done? 8. You roll a fair tetrahedron 5 times and record the sequence. possible? (a) How many sequences are (b) How many sequences containing exactly 2 fours are The answer is greater than 100) possible? (Hint: (c) How many sequences contain exactly 3 fours? (d) How many sequences contain at least 1 four? 9. Let n be a natural number and r a natural number such that 0< r < n. We have the following facts regarding the Combination formula.

Answer 1

8 novels and 7 math books. a) 6books to a friend, total 15 books in 156 ways = 5005 6) 3 novels, Ymath in & x2 = 1960 ways 6) At least 13 books 156 13 + 154 + 1 in =121 ways wwUK 0 d) At least 3 books in (15 cz + 15cht (Sest . . - 150 = (215_1-15-105) = 25-121 = 32647 ways e) Чта, Орел In Bey x?cy = 2450 ways I io children, "identical toys in 10 = 210 ways

③ a) Ternatedion has 2 1, 2, 3, 48 as outcomes at Splaces, possible outcomes = 4 =1024 ways. b Exactly a four y a ET 3 x 3 x 3 The three places can be filled in 27 ways Two us can be ananged in sc ways. - in 5 places By hndamental principle of counting total ways 56 827 = 210 ways. c) Exactly 3 fours. n y 4 a b Scz X9 = 90 ways d) At least I four no fours x 3 x 3 x 3 x3 = 0 At least I four a 1024-243 = 781 ways I = 243 ways