A restaurant offers a combo meal. A combo comes with any one of 8 sandwiches, a
ID: 3004534 • Letter: A
Question
A restaurant offers a combo meal. A combo comes with any one of 8 sandwiches, a side (there are 4 from which to choose, and a drink. There are 9 drinks you can select. How many combos are possible? How many combos are possible that have onion petals as a side? How many combos are possible that have either onion petals as a side or Fountain Dew to drink? From Peanuts: "A library shelf contains seven books. Three books are math books and four are science books. In how many ways can the books be arranged so that the math books are all together?" (Peppermint Patty's response is "DEFENSE! DEFENSE!" I would recommend giving a more carefully-thought out answer than hers) In how many ways can the letters in "HOUSE" be arranged if there are no restrictions? the vowels must be together? no two vowels are adjacent? no two consonants are adjacent? A card is drawn randomly from a deck of cards and then a second card is drawn. How many different pairs are there if the order in which cards are drawn is considered important? (i.e., drawing K , then 7 is different than 7 , then K ) How many different pairs are there if the order in which cards are drawn is not considered important? Assuming the order is important, in how many ways can the cards be selected if two kings are drawn? two hearts are drawn? a heart and a diamond are drawn? at least one ace is drawn? exactly one 10 and exactly one heart is drawn? How many integers in {1,2,3,...,300} are divisible by 3? divisible by 5? divisible by neither 3 or 5?Explanation / Answer
Post multiple question to get the remaining answers
Q1)
a) How many combos are possible?
Number of combos = 8 (number of sandwhiches) * 4 (number of sides) * 9 (number of drinks)
=> 8 * 4 * 9
=> 288 ways
b) Number of combos with onion petal as side
Number of combos = 8 (number of sandwhiches) * 1 (side must be onion petals) * 9 (number of drinks)
=> 8 * 9
=> 72 ways
c) Number of combos with either onion petal or fountain dew as drink
Number of combos possible = number of combos with onion petal + number of combos with fountain dew - number of combos with both onion petal and fountain dew
=> 8 * 1 * 9 + 8 * 4 * 1 - 8 * 1 * 1
=> 72 + 32 - 8
=> 96 ways
2) Let us tie all the maths books and make it one book,then there are 4 science book and 1 math book of (3 books)
Number of ways = 5! (arranging 5 books) * 3! (rearranging 3 maths book between each other)
=> 120 * 6
=> 720 ways
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