Practice Questions Permutations and combinations May 21, 2014

1. Use tree diagrams to answer the following:a) How many different soccer uniforms are possible if there is a choice of two typesof shirts, three types of shorts, and two types of socks?b) How many different three-scoop cones can be made from vanilla, chocolate, andstrawberry ice cream?

2. A grade 9 student may build a timetable by selecting one course for each period, with no duplication of courses. Period 1 must be science, geography, or physical education. Period 2 must be art, music, French, or business. Periods 3 and 4 must each be mathematics or English.a) Construct a tree diagram to illustrate the choices for a student’s timetable.b) How many different timetables could a student choose?

3. A standard die is rolled five times. How many different outcomes are possible?

4. A large room has a bank of five windows. Each window is either open or closed. Howmany different arrangements of open and closed windows are there?

5. Canadian postal code uses six characters. The first, third, and fifth are letters, while the second, fourth, and sixth are digits. How many codes are possible.

6. In how many ways could you choose two fives, one after the other, from a deck of cards?b) In how many ways could you choose a red five and a spade, one after the other?c) In how many ways could you choose a red five or a spade?d) In how many ways could you choose a red five or a heart?

7. In how many ways can you arrange the letters of the word think so that the t and theh are separated by at least one other letter?

8. In how many ways could ten questions on a test be arranged, if the easiestquestion and the most difficult questiona) are side-by-side?b) are not side-by-side?

9. How many 7-digit even numbers less than 3 000 000 can beformed using all the digits 1, 2, 2, 3, 5, 5, 6

10. A survey of 1000 television viewers conducted by a local television station produced the following data:• 40% watch the news at 12 00• 60% watch the news at 18 00• 50% watch the news at 23 00• 25% watch the news at 12 00 and at 18 00• 20% watch the news at 12 00 and at 23 00• 20% watch the news at 18 00 and at 23 00• 10% watch all three news broadcasts

a) What percent of those surveyed watch at least one of these programs?b) What percent watch none of these news broadcasts?c) What percent view the news at 12 00 and at 18 00, but not at 23 00?d) What percent view only one of these shows?e) What percent view exactly two of these shows?

11. There are 18 students involved in the class production of Arsenic and Old Lace.a) In how many ways can the teacher cast the play if there are five male roles andseven female roles and the class has nine male and nine female students?

b) In how many ways can the teacher cast the play if Jean will play the youngfemale part only if Jovane plays the male lead?

c) In how many ways can the teacher cast the play if all the roles could be playedby either a male or a female student?

12. A large sack contains six basketballs and five volleyballs. Find the number of combinations of four balls that can be chosen from the sack ifa) they may be any type of ballb) two must be volleyballs and two mustbe basketballsc) all four must be volleyballsd) none may be volleyballs

13. A card is randomly selected from a standard deck of cards. What is the probability that either a heart or a face card (jack, queen, or king) is selected?