SECTION 7.3 PROBLEM SET: PERMUTATIONS Do the following problems using permutations. How many three-letter words can be made 2) A grocery store has five checkout counters, and using the letters {a, b, c, d, e} if no repetitions seven clerks. How many different ways can are allowed? the 7 clerks be assigned to the 5 counters? 3) A group of fifteen people who are members of 4) Compute the following. an investment club wish to choose a president, and a secretary. How many different ways can a) 9P2 this be done? b) 6P4 c) 8P3 d) 7P4 5) In how many ways can the letters of the word 6) How many permutations of the letters of the CUPERTINO be arranged if each letter is used word PROBLEM end in a vowel? only once in each arrangement? 7) How many permutations of the letters of the 8) How many permutations of the letters word SECURITY end in a consonant? PRODUCT have consonants in the second and third positions?SECTION 7.3 PROBLEM SET: PERMUTATIONS Do the following problems using permutations. How many three-digit numbers are there? 10) How many three-digit odd numbers are there? 11) In how many different ways can five people be | 12) In how many different ways can five people be seated in a row if two of them insist on sitting seated in a row if two of them insist on not next to each other? sitting next to each other? 13) In how many ways can } English, 3 history, 14) In how many ways can 3 English, 3 history, and 2 math books be set on a shelf, if the and 2 math books be set on a shelf, if they are English books are seton the left, history books grouped by subject? in the middle, and math books on the right? 15) You have 5 math books and 6 history books to 16) You have 5 math books and 6 history books to put on a shelf with five slots. In how many put on a shelf with five slots. In how many ways can you put the books on the shelf if the ways can you put the books on the shelf if the first two slots are to be filled with math books first two slots are to be filled with the books of and the next three with history books? one subject and the next three slots are to be filled with the books of the other subject?SECTION 7.3 PROBLEM SET: PERMUTATIONS Do the following problems using permutations. 17) A bakery has 9 different fancy cakes. In how 18) A landscaper has 6 different flowering plants. many ways can 5 of the 9 fancy cakes be lined She needs to plant 4 of them in a row in a up in a row in the bakery display case? garden. How many different ways can 4 of the 6 plants be arranged in a row? 19) At an auction of used construction vehicles, 20) A landscaper has 6 different flowering plants there are \\ different vehicles for sale. In how and 4 different non-flowering bushes. She many orders could there 7 vehicles be listed needs to plant a row of 6 plants in a garden. in the auction prograph? There must be a bush at each end, and four flowering plants in a row in between the bushes. How many different arrangements in a row are possible? 21) In how many ways can all 7 letters of the 22) a. In how many ways can the letters word QUIETLY be arranged if the letters ABCDEXY be arranged if the X and Y Q and U must be next to each other in the must be next to each other in either order XY order QU? or YX? b. In how many ways can the letters ABCDEXY be arranged if the X and Y can not be next to each other