Question

Building Numbers with Specified Digits In Exercises 45-48, counting numbers are to be formed using only the digits 3, 4, and 5. Determine the number of different possibilities for each type of number described. 45. two-digit numbers 46. odd three-digit numbers 47. four-digit numbers with one pair of adjacent 4s and no other repeated digits (Hint: You may want to split the task of designing such a number into three parts, such as Part I position the pair of 4s, Part 2 position the 3, and Part 3 position the 5.) 48. five-digit numbers beginning and ending with 3 and with unlimited repetitions allowed Selecting Dinner Items The Gourmet de Coeur Restaurant offers five choices in the soup and salad category (two soups and three salads), two choices in the bread category, and four choices in the entrée category. Find the number of dinners available in each case.

Answer 1

Solution:- Digits = 3,4,5 3ways 2 ways Total 2-digit numbers = 3x2 = 16 I 47) 47) I only 3005 for odd number Total 3-digit numbers - 1x2x2 = 4 ways Asume pair of a as a single unit Total ways = 3x2x) = [6 ways i Asum only 3 only's repetition are Total ways = 1x3x3x371 = repetition are " allowed only s 127 ways salads 49) Total ways too dinner = 2x 3 x 2 x - 4 Bread onto ei soup " = [ 48 ] ways